### ALL Questions

## Two identical discs of mass m and of radius R touch each other and move with the same velocity perpendicularly to the line segment which joins their centres of mass, along the surface of a horizontal smooth tabletop. There is a third disc of mass M and of radius R at rest, at a point on the perpendicular bisector of the line segment joining the centres of mass of the two moving discs as shown in the figure. The two moving discs collide elastically with the third one, which is at rest. There is no friction between the rims of the discs. What should the ratio of M/m be in order that after the collision the two discs of mass m move perpendicularly to their initial velocity?

Two identical discs of mass m and of radius R touch each other and move with the same velocity perpendicularly to the line segment which joins their centres of mass, along the surface of a horizontal smooth tabletop. There is a third disc of mass M and of radius R at rest, at a point on the perpendicular bisector of the line segment joining the centres of mass of the two moving discs as shown in the figure. The two moving discs collide elastically with the third one, which is at rest. There is no friction between the rims of the discs. What should the ratio of M/m be in order that after the collision the two discs of mass m move perpendicularly to their initial velocity?

## A triangular frame consists of three identical rods, each of mass m and length l. It rests upright on a horizontal smooth surface with its lower right corner against a stop about which the frame could pivot. A horizontal force of magnitude F is applied to the upper corner of theframe as shown in the figure. What is the largest value of F may have without causing the frame to pivot upward about the stop?

A triangular frame consists of three identical rods, each of mass m and length *l*. It rests upright on a horizontal smooth surface with its lower right corner against a stop about which the frame could pivot. A horizontal force of magnitude F is applied to the upper corner of the

frame as shown in the figure. What is the largest value of F may have without causing the frame to pivot upward about the stop?

## A particle is moving along straight line such that dot product of its acceleration and velocity is negative. How many times particle can be found at a distance d from the origin?

A particle is moving along straight line such that dot product of its acceleration and velocity is negative. How many times particle can be found at a distance d from the origin?

## A uniform, solid cylinder having mass M and radius R is pulled by a horizontal force F acting through the center as shown. The cylinder rolls to the right without slipping. What is the magnitude of the force of friction between the cylinder and the ground?

A uniform, solid cylinder having mass M and radius R is pulled by a horizontal force F acting through the center as shown. The cylinder rolls to the right without slipping. What is the magnitude of the force of friction between the cylinder and the ground?

## An object of mass M starts from rest at the bottom of a fixed incline of height H. A person decides to push the object up the incline in one of two ways with an applied force shown in the diagram. In each of the trials, the object reaches the top of the incline with speed V. How would the work done by the person on the block compare for the two trials? Assume the same constant non-zero coefficient of kinetic friction between the incline and the object for both trials.

An object of mass M starts from rest at the bottom of a fixed incline of height H. A person decides to push the object up the incline in one of two ways with an applied force shown in the diagram. In each of the trials, the object reaches the top of the incline with speed V. How would the work done by the person on the block compare for the two trials? Assume the same constant non-zero coefficient of kinetic friction between the incline and the object for both trials.

## The position versus time graph of a particle moving along a straight line is shown. What is the total distance travelled by the particle from t = 0 s to t = 10s?

The position versus time graph of a particle moving along a straight line is shown. What is the total distance travelled by the particle from t = 0 s to t = 10s?

## A wedge of mass M= 10kg, height h= 3m and angle of inclination is at rest at horizontal surface. There is a small point – like object (mass m = 0.5kg) next to the slope as shown in the figure. At what acceleration must wedge be moved in order that the point like object reaches its top in a time t = 5s (Neglect the friction between point like object and wedge)

A wedge of mass M= 10kg, height h= 3m and angle of inclination is at rest at horizontal surface. There is a small point – like object (mass m = 0.5kg) next to the slope as shown in the figure. At what acceleration must wedge be moved in order that the point like object reaches its top in a time t = 5s (Neglect the friction between point like object and wedge)

## Ram pushes eight identical blocks on the horizontal frictionless surface with horizontal force F. The force that block-1 exerts at block-2 has magnitude and the force that block-7 exerts on the block-8 is

Ram pushes eight identical blocks on the horizontal frictionless surface with horizontal force F. The force that block-1 exerts at block-2 has magnitude and the force that block-7 exerts on the block-8 is

## Find velocity of piston A in the given situation if angular velocity of wheel of radius R is (constant), in the clockwise sense. (O is fixed point)

Find velocity of piston A in the given situation if angular velocity of wheel of radius R is (constant), in the clockwise sense. (O is fixed point)

## An ideal string-pulley system is shown in the figure and system is released from rest. Choose correct option.

An ideal string-pulley system is shown in the figure and system is released from rest.

Choose correct option.

## A two stage rocket is fired vertically upward from rest with acceleration as shown in a-t graphs. After 15 sec, the first stage burns out and second stage ignites. Choose the INCORRECT statement regarding motion of rocket in the time interval

A two stage rocket is fired vertically upward from rest with acceleration as shown in a-t graphs. After 15 sec, the first stage burns out and second stage ignites. Choose the INCORRECT statement regarding motion of rocket in the time interval

## One end of a heavy uniform rod AB can slide along rough horizontal guiding surface CD with the help of massless ring as shown in the figure. The dimension of ring is negligible. BE is the ideal string. If is right angle and is the angle between rod AB and horizontal when the rod is on the verge of sliding. Find the coefficient of friction between ring and horizontal guiding surface CD.

One end of a heavy uniform rod AB can slide along rough horizontal guiding surface CD with the help of massless ring as shown in the figure. The dimension of ring is negligible. BE is the ideal string. If is right angle and is the angle between rod AB and horizontal when the rod is on the verge of sliding. Find the coefficient of friction between ring and horizontal guiding surface CD.

## A man of mass 60 kg hangs himself from a massless spring balance, which itself suspended from an ideal string-pulley system as shown in thefigure. The string AB can bear maximum 900 N. Choose correct statement.

A man of mass 60 kg hangs himself from a massless spring balance, which itself suspended from an ideal string-pulley system as shown in the

figure. The string AB can bear maximum 900 N. Choose correct statement.

## A uniform solid hemisphere of radius 10 m and mass 64 kg is placed with its curved surface on the smooth horizontal surface and a string AB of length 4m is attached to point A on its rim as shown in the figure. Find the tension in the string if hemisphere is in equilibrium.

A uniform solid hemisphere of radius 10 m and mass 64 kg is placed with its curved surface on the smooth horizontal surface and a string AB of length 4m is attached to point A on its rim as shown in the figure. Find the tension in the string if hemisphere is in equilibrium.

## A uniform rod of mass M and length L is free to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the rod rotating clockwise about the pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its center of mass?

A uniform rod of mass M and length L is free to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the rod rotating clockwise about the pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its center of mass?

## An object is being pushed at constant speed on an inclined plane. The free body diagram of the object is shown with the gravitational force represented by W, the friction force by f, the applied external push parallel to the incline by F, and the normal force with surface by N. Which one of the following choices represents correct relationships between the forces?

An object is being pushed at constant speed on an inclined plane. The free body diagram of the object is shown with the gravitational force represented by W, the friction force by f, the applied external push parallel to the incline by F, and the normal force with surface by N. Which one of the following choices represents correct relationships between the forces?

## A string of mass m (can be non uniform as well) is suspended through two points which are not in same horizontal level. Tension in the string at the end points are T1 and T2 and at the lowest point is T3. Mass of string in terms of T1, T2 and T3 can be represented a {uniform gravity ‘g’ exists downwards)

A string of mass m (can be non uniform as well) is suspended through two points which are not in same horizontal level. Tension in the string at the end points are T1 and T2 and at the lowest point is T3. Mass of string in terms of T1, T2 and T3 can be represented a {uniform gravity ‘g’ exists downwards)

## All the blocks are attached to an ideal rope which passes over an ideal pulley. If accelerations of blocks m1, m2, m3, and m4 are a1, a2, a3 and a4 respectively then choose the correct option.

All the blocks are attached to an ideal rope which passes over an ideal pulley. If accelerations of blocks m1, m2, m3, and m4 are a1, a2, a3 and a4 respectively then choose the correct option.

## A massless spring of stiffness 400 N/m is fastened at left end to a vertical wall as shown in the figure I. Initially block C of mass 2 kg and block D of mass 5 kg rest on horizontal surface with block C in contact with spring (But not compressing it.) and the block D in contact with block C. Block C is moved leftward, compressing spring by a distance of 0.5 m and held in place while block D remains at rest as shown in the figure. Now Block C is released block D. The surface is rough and the coefficient of friction between each block and surface is 0.1. The block collide instantaneously stick together and move right. Find the velocity of combined system just after collision.

A massless spring of stiffness 400 N/m is fastened at left end to a vertical wall as shown in the figure I. Initially block C of mass 2 kg and block D of mass 5 kg rest on horizontal surface with block C in contact with spring (But not compressing it.) and the block D in contact with block C. Block C is moved leftward, compressing spring by a distance of 0.5 m and held in place while block D remains at rest as shown in the figure.

Now Block C is released block D. The surface is rough and the coefficient of friction between each block and surface is 0.1. The block collide instantaneously stick together and move right. Find the velocity of combined system just after collision.

## The mean of the numbers a ,b ,8 ,5 ,10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

The mean of the numbers a ,b ,8 ,5 ,10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

## The average marks of boys in class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is ?

The average marks of boys in class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is ?

## Suppose a population A has 100 observations 101,102, ..., 200, and another population B has 100 observations 151, 152, ..., 250. If VA and VB represent the variances of the two populations, respectively 1then VA /VB is

Suppose a population A has 100 observations 101,102, ..., 200, and another population B has 100 observations 151, 152, ..., 250. If VA and VB represent the variances of the two populations, respectively 1then VA /VB is

## Let x1, x2, ...., xn be n observations such that and .Then a possible value of n among the following is

Let x1, x2, ...., xn be n observations such that and .Then a possible value

of n among the following is

## In a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

In a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

## In a series of 2n observations, half of them equal a and remaining half equal – a. If the standard deviation of the observations is 2, then |a| equals

In a series of 2n observations, half of them equal a and remaining half equal – a. If the standard deviation of the observations is 2, then |a| equals

## Consider the following statements : (1) Mode can be computed from histogram (2) Median is not independent of change of scale (3) Variance is independent of change of origin and scale. Which of these is/are correct?

Consider the following statements :

(1) Mode can be computed from histogram

(2) Median is not independent of change of scale

(3) Variance is independent of change of origin and scale.

Which of these is/are correct?

## The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

## In an experiment with 15 observations on x, the following results were available. One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is

In an experiment with 15 observations on x, the following results were available.

One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is

## In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?

## Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then what will be the distance covered by the smaller body just before the collision?

Two spherical bodies of mass *M* and 5*M* and radii *R* and 2*R* respectively are released in free space with initial separation between their centres equal to 12*R*. If they attract each other due to gravitational force only, then what will be the distance covered by the smaller body just before the collision?

## The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, what will be the new time period?

The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, what will be the new time period?

## The escape velocity of a body depends upon mass as

The escape velocity of a body depends upon mass as

## What is the kinetic energy needed to project a body of mass m from the earth's surface (radius R) to infinity?

What is the kinetic energy needed to project a body of mass m from the earth's surface (radius R) to infinity?

## What is the energy required to move a body of mass m from an orbit of radius 2R to 3R?

What is the energy required to move a body of mass *m* from an orbit of radius *2R* to *3R? *

## If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

## For the given uniform square lamina ABCD, whose centre is O,

For the given uniform square lamina *ABCD*, whose centre is O,

## Angular momentum of the particle rotating with a central force is constant due to

Angular momentum of the particle rotating with a central force is constant due to

## A round uniform body of radius R, mass M and moment of inertia I rolls down (without slipping) an inclined plane making an anglewith the horizontal. Then what will be its acceleration?

A round uniform body of radius *R*, mass *M* and moment of inertia *I* rolls down (without slipping) an inclined plane making an anglewith the horizontal. Then what will be its acceleration?

## A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is from the centre of the bigger disc. What is the value of ?

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is from the centre of the bigger disc. What is the value of ?

## Four point masses, each of value m, are placed at the corners of a square ABCD of side l. What will be the moment of inertia of this system about an axis through A and parallel to BD?

Four point masses, each of value *m*, are placed at the corners of a square *ABCD* of side *l*. What will be the moment of inertia of this system about an axis through *A* and parallel to *BD? *

## A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity

A thin circular ring of mass *m* and radius *R* is rotating about its axis with a constant angular velocity Two objects each of mass *M* are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity

## A force ofacts on O, the origin of the coordinate system. What is the torque about the point (1, –1)?

A force ofacts on *O*, the origin of the coordinate system. What is the torque about the point (1, –1)?

## Consider a two-particle system with particles having masses m1 and m2. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

Consider a two-particle system with particles having masses m_{1} and m_{2}. If the first particle is pushed towards the centre of mass through a distance *d*, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

## A T shaped object with dimensions shown in the figure is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. What is the location of P with respect to C?

A *T* shaped object with dimensions shown in the figure is lying on a smooth floor. A force *F* is applied at the point *P *parallel to *AB*, such that the object has only the translational motion without rotation. What is the location of *P* with respect to *C? *

## A thin rod of length L is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as k(x/L)n where n can be zero or any positive number. If the position xCM of the centre of mass of the rod is plotted against n, which of the following graphs best approximates the dependence of xCM on n?

A thin rod of length *L* is lying along the *x*-axis with its ends at *x* = 0 and *x* = *L*. Its linear density (mass/length) varies with *x* as *k*(*x*/L)^{n} where *n* can be zero or any positive number. If the position *x*_{CM} of the centre of mass of the rod is plotted against *n*, which of the following graphs best approximates the dependence of *x*_{CM} on *n*?