Question & Answer

A wheel rotates with a constant acceleration of 2.0 radian/sec2. It the wheel starts from rest, the number of revolutions it makes in the first ten seconds will be approximately

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is

A torque of 30 N-m is applied on a 5 kg wheel whose moment of inertia is 2kg-m2 for 10 sec. The angle covered by the wheel in 10 sec will be

A constant torque of 1000 N -m, turns a wheel of moment of inertia 200 kg -m2 about an axis passing through the centre. Angular velocity of the wheel after 3 s will be

A particle performs uniform circular motion with an angular momentum L. If the frequency of a particle's motion is doubled and its kinetic energy is halved, the angular momentum becomes.

Let P = (–1, 0), Q = (0, 0) and R =  be three points. What is the equation of the bisector of the angle PQR?

An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver?

Let A(h, k), B(1, 1) and C(2, 1) be the vertices of a right-angled triangle with AC as its hypotenuse. If the area of the triangle is 1 square unit, then the set of values which ‘k’ can take is given by

The angular momentum of a system of particles is conserved

The equation of a tangent to the parabola y² = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

For the Hyperbola  which of the following remains constant when a varies?

If (a, a²) falls inside the angle made by the lines, y = x/2, x > 0 and y = 3x, x > 0, then a belongs to

Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of chord of the circle C that subtend an angle of  at its centre is

If the lines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area  square units, then what will be the equation of the circle?

In an ellipse, the distance between its focii is 6 and the minor axis is 8. Then its eccentricity is,

The locus of the vertices of the family of parabolas  is

A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A. Its equation is,

If the pair of lines ax² + 2(a + b)xy + by² = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then

The locus of a point  moving under the condition that the line  is a tangent to the hyperbola  is

An ellipse has OB as semi-minor axis, F and F' its focii and the angle FBF' is a right angle. Then what will be the eccentricity of the ellipse?

If a circle passes through the point (a, b) and cuts the circle x² + y² = p² orthogonally, then the equation of the locus of its centre is

A circle touches the x­-axis and also touches the circle with centre at (0, 3) and radius 2. What will be the locus of the centre of the circle?

A particle of mass 4 m which is at rest explodes into three fragments, two of the fragments each of mass m are found to move each with a speed v making an angle 90 with each other. The total energy relased in this explosion is -

A slow moving electron collides elastically with a hydrogen atom at rest. The initial and final motions are along the same straight line. What fraction of electron's kinetic energy is transferred to the hydrogen atom? The mass of hydrogen atom is 1850 times the mass of electron?

If the circles x² + y² + 2ax + cy + a = 0 and x² + y² – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x+by – a = 0 passes through P and Q for

If a vertex of a triangle is (1, 1) and the midpoints of two sides through this vertex are (–1, 2) and (3, 2), then what will be the centroid of the triangle.

If non ­zero numbers a, b, c are in H.P., then the straight line  always passes through a fixed point. That point is

The line parallel to thex­axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx – 2ay – 3a = 0, where (a, b)  (0, 0) is

Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of midpoint of PQ is

The mass of a rocket is 500 kg and the relative velocity of the gases ejecting from it is 250 m/s with respect to the rocket. The rate of burning of the fuel in order to give the rocket an initial acceleration 20 m/s2 in the vertically upward direction (g = 10 m/s2), will be

A 20 g bullet pierces through a plate of mass m1 = 1 kg and then comes to rest inside a second plate of mass m2 = 2.98 kg. It is found that the two plates, initially at rest, now move with equal velocities. The percentage loss in the initial velocity of bullet when it is between m1 and m2. (Neglect any loss of material of the bodies, due to action of bullet.) will be

If the straight lines x = 1 + s, y = –3  z = 1 +  and x = t/2, y = 1 + t, z = 2 – t, with parameters s and t respectively, are co­planar, then  equals

A bullet of mass 10g travelling horizontally with a velocity of 300 m/s strikes a block of wood of mass 290 g which rests on a rough horizontal floor. After impact the block and the bullet move together and come to rest when the block has travelled a distance of 15 m. The coefficient of friction between the block and the floor will be - (Duration of impact is very short)

The eccentricity of an ellipse, with its centre at the origin, is 1/2. If one of the directrices is x = 4, then the equation of the ellipse is

The intercept on the line y = x by the circle x² + y² – 2x = 0 is AB. Equation of the circle on AB as diameter is

If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference  then the equation of the circle is

If a  0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then