PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions for Physics

Two concentric spherical shells have masses M₁, M₂ and radii R₁, R₂ (R₁ < R₂). What is the force exerted by this system on a particle of mass m₁ if it is placed at a distance (R₁+ R₂)/2 from the centre?

A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the centre.

A tunnel  is dug along a chord of the earth at a perpendicular distance R/2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. Find the force exerted by the wall on a particle of mass m when it is at a distance x from the centre of the tunnel.

A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in the following figure . A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if (a) r < x < 2r, (b) 2r < x < 2R and (c) x > 2R.

Consider the situation shown in the following figure. The system is released from rest and the block of mass 1 kg is found to have a speed 0⋅3 m/s after it has descended a distance of 1 m. Find the coefficient of kinetic friction between the block and the table.

A uniform metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4a (In the following figure). The centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P₁ and P₂ shown in the figure.

A thin spherical shell having uniform density is cut in two parts by a plane and kept separated as shown in the following figure. The point A is the centre of the plane section of the first part and B is the centre of the plane section of the second part. Show that the gravitational field at A due to the first part is equal in magnitude to the gravitational field at B due to the second part.

A block of mass 100 g is moved with a speed of 5⋅0 m/s at the highest point in a closed circular tube of radius 10 cm kept in a vertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations inside the tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.

A particle of mass 100 g is kept on the surface of a uniform sphere of mass 10 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle away from the sphere.

A small block of mass 200 g is kept at the top of a frictionless incline which is 10 m long and 3⋅2 m high. How much work was required (a) to lift the block from the ground and put it an the top, (b) to slide the block up the incline? What will be the speed of the block when it reaches the ground if (c) it falls off the incline and drops vertically to the ground (d) it slides down the incline? Take g = 10 m/s². 

The gravitational field in a region is given by \[E = \left( 2 \overrightarrow{i} + 3 \overrightarrow{j} \right) N {kg}^{- 1}\] . Show that no work is done by the gravitational field when a particle is moved on the line 3y + 2x = 5.

A block weighing 10 N travels down a smooth curved track AB joined to a rough horizontal surface (In the following figure). The rough surface has a friction coefficient of 0⋅20 with the block. If the block starts slipping on the track from a point 1⋅0 m above the horizontal surface, how far will it move on the rough surface?

A particle executing simple harmonic motion comes to rest at the extreme positions. Is the resultant force on the particle zero at these positions according to Newton's first law?

Can simple harmonic motion take place in a non-inertial frame? If yes, should the ratio of the force applied with the displacement be constant?

A particle executes simple harmonic motion. If you are told that its velocity at this instant is zero, can you say what is its displacement? If you are told that its velocity at this instant is maximum, can you say what is its displacement?

A block of mass 5 kg is suspended from the end of a vertical spring which is stretched by 10 cm under the load of the block. The block is given a sharp impulse from below, so that it acquires an upward speed of 2 m/s. How high will it rise? Take g = 10 m/s².