IIT JAM Physics Mock Test - 4 - Physics MCQ

Two blocks of masses 3 kg and 4 kg are hung from the ceiling by three cables as shown.

The cable in the middle is exactly horizontal and the cable on the left makes an angle of 45° with respect to the vertical. The angle θ made by the cable on the right with respect to the vertical is

A man climbs down a hemispherical hill of radius 50 m from the topmost point. If the coefficient of friction between the shoes and the hill is μ = 0.05, then approximately how much distance does he have to walk before he slips?

Two satellites S₁, and S₂ revolve round a planet in coplanar circular orbit in the same sense. Their periods of revolutions are 1 hour and 8 hour respectively. The radius of the orbit of S₁, = 10⁴ km. When S₂ is closest to S₁ then the angular speed of S₂ as obseived by an astronaut in S₁.

Assume a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to R-^3/2, then T is proportional to

Consider a spherical planet rotating about an axis passing through its centre. The velocity of a point on its equator is three-forth of the value of g measured at one of the poles, then the escape velocity for a particle shot upwards from that pole will be

A particle with time-varying mass 

where are positive constants, moves along the x-axis under the action of a constant positive force F for f the particle is at rest at time t = 0. then at time t. its velocity V will be —

The kinetic energy of body is increased by 44%. What isthe percentage increase in the magnitude of linear momentum of the body?

A point particle at rest is released from the top of a sphere of radius R and slides down frictionlessly under gravity. At what angle from the vertical does it leave the sphere?

Three masses m 2m and 3m are moving in x - y plane with speeds 3u, 2u ad u respectively, as shown in the figure. The velocity of the resulting mass would be

A mass of 1 kg moving with a speed 4 m/sec, hits another mass 2 kg moving in the same direction with a speed of 2 m/sec, then Kinetic energy of the centre of mass is

A block of mass 1 kg is initially held at rest on the frictionless surface of a wedge of mass 10 kg. The wedge itself lies on horizontal frictionless surface. The block is now released so that it is allowed to slide down the slope. How far down the slope does the block move when the wedge has moved a distance of 20 cm?

A ball of mass m moving at a speed V makes a head on collision with an identical ball at rest. The kinetic energy of the balls after the collision is 1/2 th of the original. Find the coefficient of restitution.

Four masses each of mass m are at the corners of a square of side a as shown in the figure. The product of inertia I_xy of the system about O is

A hollow sphere of moment of inertia 2/3 MR² and a thin loop of moment of inertia MR² roll without slipping down an inclined plane. The ratio of their times of arrival   at the bottom of the incline is given by

Consider the uniform solid right cone depicted in the figure on the right. This cone has mass m and a circular base of radius r. If the moment of inertia of the cone about an axis parallel to the x axis passing through the centre of mass O_cm (see figure) is given by

Then the moment of inertia about another axis parallel to the x axis, but passing through the point 0_r ( (see figure), is

Three identical rings of radius a are placed on the xy-plane so that each ring touches tine other two tangentially. Each ring, which may be considered to be infinitesimally thin, has a mass M. The centres of three equidistant from the z-axis this common distance being 2a/√3 . What is the moment of inertia of this  system about the z-axis.

I f pressure at half the depth of a lake is equal to  2/3 pressure at the bottom of the  lake then what is the depth of the lake.

The directed beam from a small but powerful searchlight placed on the ground tracks a small plane flying horizontally at a fixed height h above the ground with a uniform velocity V as shown in the figure below.

If the searchlight starts rotating with an instantaneous angular velocity ω₀ at time t = 0 when the plane was directly overhead, then at a later time t its instantaneous angular velocity ω(t) is given by

A ball is dropped vertically from a height H on to a plane surface and permitted to bounce repeatedly along a vertical line. After every bounce, its kinetic energy becomes a quarter of its kinetic energy before the bounce. The ball will come to rest after time

A horizontally placed hollow tube has a cross-sectional Area A at the beginning of the tube that gradually tapers off to A/2 at the end. An incompressible, ideal fluid of density p enters the tube with a velocity V at the beginning of the tube. What is the difference in pressure at the two ends of the tube?

A solid sphere of mass m and radius r is released from rest at point A on a track in vertical plane. The track is rough enough to support rolling between A and B and from B onwards it is smooth. The maximum height attained by sphere from ground on its journey from B onwards is

The pulley shown in figure has moment of ineitia I about its axis and radius R. Find the acceleration of two blocks.

A force F acts tangentially at the highest point of a solid sphere of mass m kept on a rough horizontal plane. If the sphere rolls without slipping. Find the acceleration of the centre of sphere.

A particle of mass m is thrown upward with velocity V and there is retarding air resistance proportional to the square of the velocity with proportionality constant K. If the particle attains a maximum height after time t and g is the gravitational acceleration, what is the velocity?

A small spherical ball is released from a point at a height h on a rough block shown in figure. Assuming that it does not slip anywhere, find its linear speed when it rolls on the horizontal part of the track?

An xyz coordinate system is rotating with respect to an xyz coordinate system. The angular velocity of the xyz system relative to the xyz system is given by  where t is time. The position vector   then Coriolis acceleration at time t = 1 sec is

On the opposite sides of a wide vertical vessel filled with water two identical holes are opened each having the cross sectional area a=0.50 cm². The height difference between them is equal to Δh = 50 cm. Find the resultant force of reaction of the water flowing out of the vessel.