MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions

A particle is moving with speed v = b`sqrtx` along positive x-axis. Calculate the speed of the particle at time t = τ (assume that the particle is at origin at t = 0).

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 α/R form the centre of the bigger disc. The value of α is ______.

A satellite is revolving in a circular orbit at a height 'h' above the surface of the earth of radius 'R'. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between 'h' and 'R' is ______.

The ratio of binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height h above the earth's surface is ______ (R = radius of the earth).

Let M be the mass and L be the length of a thin uniform rod. In first case, axis of rotation is passing through centre and perpendicular to the length of the rod. In second case, axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case is ______.

For a perfectly black body, the graph is plotted between the frequency of the radiation with maximum intensity (v_m) and the absolute temperature T. Out of the following, which is the correct graph?

A satellite revolves around a planet very close to its surface. By what maximum factor can its kinetic energy be increased suddenly, such that it revolves in orbit in the same way?

A parallel plate capacitor is charged to 100 × 10^-6 C. Due to radiations, falling from a radiating source, the plate loses charge at the rate of 2 × 10^-7 Cs^-1. The magnitude of displacement current is ______.

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d₁​ and d₂​ are filled in the tube. Each liquid subtends 90° angle at centre. Radius joining their interface makes an angle α with vertical. Ratio ​d₁/d₂​​ is ______.

A person throws a ball with a speed of 10 m/s at an angle of 30° with horizontally from the top of a 10 m high tower. The distance of the ball from the foot of the tower after falling on the ground will be ______.

A satellite is revolving around a planet in a circular orbit close to its surface and ρ is the mean density and R is the radius of the planet, then the period of ______.

(G = universal constant of gravitation)

Two satellites are orbiting around the earth in circular orbits of same radius. One of them is 10 times greater in mass than the other. Their period of revolutions are in the ratio ______.

The ratio of the radii of gyration of a circular disc and a circular ring of the same radius about a tangential axis in the plane is ______.

Two satellites of same mass are orbiting round the earth at heights of r₁ and r₂ from the centre of earth. Their potential energies are in the ratio of ______.

A soap bubble of radius 2.0 cm is formed inside another soap bubble of radius 4.0 cm. The radius of another soap bubble which has the same pressure difference as that between the inside of the smaller and outside of large soap bubble, in metres is ______

When tension T is applied to a sonometer wire of length l, it vibrates with the fundamental frequency n. Keeping the experimental setup the same, when the tension is increased by 8 N, the fundamental frequency becomes three times the earlier fundamental frequency n. The initial tension applied to the wire (in newton) was ______.

If the flux associated with a coil changes at the rate of 360 webers every 4 minutes, then the induced e.m.f. is ______

A solid cylinder of radius r and mass M rolls down an inclined plane of height h. When it reaches the bottom of the plane, then its rotational kinetic energy is ____________.

(g = acceleration due to gravity)

The angle subtended by the vector A = `5hat"i" + 3hat"j" + 12hat"k"` with the X-axis is ______.

A uniform rod of length '6L' and mass '8 m' is pivoted at its centre 'C'. Two masses 'm' and ' 2m' with speed 2v, v as shown strikes the rod and stick to the rod. Initially the rod is at rest. Due to impact, if it rotates with angular velocity 'w₁' then 'w' will be ________.