JEE Main entrance exam Question Bank Solutions for Physics (JEE Main)

A thin circular ring of mass M and radius R is rotating with a constant angular velocity of 2 rads^-1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity (in rads^-1).

A particle of mass ‘m’ is moving in time ‘t’ on a trajectory given by

`vecr  = 10alphat^2hati + 5beta(t - 5)hatj`

Where α and β are dimensional constants.

The angular momentum of the particle becomes the same as it was for t = 0 at time t = ______ seconds.

Angular momentum of a single particle moving with constant speed along the circular path ______.

The magnitude of the torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5 m, the angle between the force and the position vector is (in radians) ______.

A solid sphere is rotating in free space. If the radius of the sphere is increased while keeping the mass the same, which one of the following will not be affected?

If the radius of the earth shrinks by 2% while its mass remains the same. The acceleration due to gravity on the earth's surface will approximately ______.

The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of the earth will, be ______.

(Radius of earth = 6400 km)

Two massless springs with spring constants 2k and 9k carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be ______.

If the frequency of light in a photoelectric experiment is doubled, the stopping potential will ______.

If Y, K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as :

I₁ = M.I. of thin circular ring about its diameter,

I₂ = M.I. of circular disc about an axis perpendicular to disc and going through the centre,

I₃ = M.I. of solid cylinder about its axis and

I₄ = M.I. of solid sphere about its diameter.

Then -

Four equal masses, m each are placed at the corners of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be ______.

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force `vec"P"` of magnitude 100 N is applied at point A of the frame.

Suppose the force is `vec"P"` resolved parallel to the arms AB and AC of the frame.

The magnitude of the resolved component along the arm AC is xN.

The value of x, to the nearest integer, is ______.

[Given: sin(35°) = 0.573, cos(35°) = 0.819, sin(110°) = 0.939, cos(110°) = –0.342]

An engine takes in 5 moles of air at 20°C and 1 atm, and compresses it adiabatically to `1/10^"th"` of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is ______.

Consider a badminton racket with length scales as shown in the figure.

If the mass of the linear and circular portions of the badminton racket is the same (M) and the mass of the threads is negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, `r/2` distance from the ends A of the handle will be ______ Mr².

A metal wire of length L, area of cross section A and Young's modulus Y behaves as a spring of spring constant k given by:

If photons of ultraviolet light of energy 12 eV are incident on a metal surface of work function of 4 eV, then the stopping potential (in eV) will be :

A diatomic molecule can be modelled as two rigid balls connected with spring such that the balls can vibrate with respect to centre of mass of the system (spring + balls). Consider a diatomic gas made of such diatomic molecule. If the gas performs 20 Joule of work under isobaric condition, then heat given to the gas is ______ J.

A body moves in a straight line along, the x-axis. Its distance x (in metre) from the origin is given by x = 8t - 3t². The average speed in the interval t = 0 to t = 1 second is ______.

The figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If x and y be the distances travelled by A and B in the same time interval, then ______.