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 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 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?

If a is square matrix of order 3 such that adja=64 find |a|

wave equation y= 0.08 sin 2pi/lambda[200t-x]

find velocity of wave

A parachutist drops freely from an aeroplane for 8s before the parachute opens out.then he descends with a retardation of 2ms reaching the ground with a velocity of 6ms.find the height from which he falls

A ball of density p0 falls from rest from point P onto the surface of a liquid of density p0 in time T. It enters the liquid stops moves up and returns to P in a total time 3T. Neglect viscosity, surface tension and splashing. The ratio p/p0 is equal to

An engine whistling at a constant frequency n0 and moving with a constant velocity goes past a stationary observer. As the engine crosses him, the frequency of the sound heard by him changes by a factor f. The actual difference in the frequency of the sound heard by him before and after the engine across him is

A flat coil of area A and n turns is placed at the centre of a ring of radius r (r2 >> A) and resistance R. The two are co-planar when current in the coil increases from zero to i, the total charge circulating in the ring is?

2 masses of 4kg and 6kg kept at a distance of 2m.Where the 3rd mass be placed,the gravitational be zero

Calculate the fringe width for light of wavelength 550 nm in a Young's slit experiment where the double slits are separated by 0.75 mm and the screen is placed 0.80 m from them.

Sample of 2,3 dibromopentane is heat in zinc dust the resulting compound is isolated and heated with hi in presence of p to yield---------

In a crystal structure of an element, atoms are present in ccp arrangement and tetrahedral voids, which of the following relation between the atomic radius and edge length is correct for the unit cell which is formed in this arrangement? (a is the edge length and R is the radius of atom)

The normal at P to a hyperbola of eccentricity e, intersects its transverse and conjugate axes at L and M respectively. If locus of the mid-point of LM is hyperbola, then eccentricity of the hyperbola is?

The focal length of the objective of a microscope is 2cm.The final image of object placed 3cm from the objective is formed at least distance of the distinct vision.if the magnifying power is 10 then calculate focal length of eyepiece.

The number of ordered pairs (x, y) of real numbers satisfying

is equal to ?

The pH of a H2 SO4 solution is 2. The pH of this solution, if equal volume of 0.2 M NaCl solution is added to it, will be:

A copper rod of length L and mass m is sliding down a smooth inclined plane of inclination with a constant speed v. A current I is flowing in perpendicular to the plane of diagram inwards. A vertically upward magnetic field B exists in this region. The magnitude of the required magnetic B is?

**A body oscillates with amplitude of 10 cm in a horizontal platform. The maximum angular frequency which the platform can vibrate vertically such that body of mass 10 kg will not leave contact is **

A long Sighted can see distinctly object beyond 1 m.Calculate the power of less for the this person for normal vision?

A uniform circular disc of masss 12 kg is held by 2 identical springs when disc is pressed down slightly and released it executes shm with time period of2 s the force constant of each spring is [2 spring in parallel]

Two blocks of masses 6kg and 4kg connected by a rope of mass 4 kg are resting on frictionless floor as shown. If a constant force of 21 Newton is applied to 6 kg block, tension (In N) in the rope at point B is (CB : BA = 1 : 1)

In a hemispherical shell of radius R, a rod of mass kg is placed horizontally. The length of rod is R. Find the normal reaction at any end of the rod (in N).

The number of solutions of

is

How many maximum number of electrons of an atom have the following set of quantum numbers? n = 4, l = 0, 1, 2, m = 0, +1, s = -1⁄2

The ratio of speed of sound wave in neon to that in water vapours at any temperature is

What is the azimuthal quantum number of the unpaired electron of chlorine?

The electron of hydrogen atom was excited from ground state to a higher orbit. During de-excitation of the electron, photons of six different wavelengths were emitted. If each photon forms a spectral line, how many spectral line will be visible to naked eye?

What is the sum of the number of electrons with l = 0 and l = 2 present in Cu+ ion?

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecule is ?

For the estimation of nitrogen, 1.4 g of an organic compound was digested by Kjeldahl method and the evolved ammonia was absorbed in 60 mL of M/10 sulphuric acid. The unreacted acid required 20 mL of M/10 sodium hydroxide for complete neutralization. The percentage of nitrogen in the compound is ?

The variance of first 50 even natural numbers is:

What is Human excretory system? explain?

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx*x where a and b are constants. The work done in stretching the unstretched rubber-band by L is ?

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 10000 V/m, the charge density of the positive plate will be close to

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100°C is ?

(For steel Young’s modulus is (2 × 10^11) N/m^2 and coefficient of thermal expansion is 1.1 × 10^-5 K^-1)

A block of mass m is placed on a surface with a vertical cross section given by

.

If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is ?

If 9th term of AP is 12 and 10the term is 18.what will be 18the term?