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

A heavy particle is suspended by a 1⋅5 m long string. It is given a horizontal velocity of \[\sqrt{57} \text{m/s}\] (a) Find the angle made by the string with the upward vertical when it becomes slack. (b) Find the speed of the particle at this instant. (c) Find the maximum height reached by the particle over the point of suspension. Take g = 10 m/s². 

In a simple harmonic motion

In a simple harmonic motion
(a) the maximum potential energy equals the maximum kinetic energy
(b) the minimum potential energy equals the minimum kinetic energy
(c) the minimum potential energy equals the maximum kinetic energy
(d) the maximum potential energy equals the minimum kinetic energy

An object is released from rest. The time it takes to fall through a distance h and the speed of the object as it falls through this distance are measured with a pendulum clock. The entire apparatus is taken on the moon and the experiment is repeated
(a) the measured times are same
(b) the measured speeds are same
(c) the actual times in the fall are equal
(d) the actual speeds are equal

A particle executes simple harmonic motion with an amplitude of 10 cm and time period 6 s. At t = 0 it is at position x = 5 cm going towards positive x-direction. Write the equation for the displacement x at time t. Find the magnitude of the acceleration of the particle at t = 4 s.

A simple pendulum of length L with a bob of mass m is deflected from its rest position by an angle θ and released (following figure). The string hits a peg which is fixed at a distance x below the point of suspension and the bob starts going in a circle centred at the peg. (a) Assuming that initially the bob has a height less than the peg, show that the maximum height reached by the bob equals its  initial height. (b) If the pendulum is released with \[\theta = 90^\circ \text{ and x = L}/2\] , find the maximum height reached by the bob above its lowest position before the string becomes slack. (c) Find the minimum value of x/L for which the bob goes in a complete circle about the peg when the pendulum is released from \[\theta = 90^\circ \]

A particle of mass m is kept on the top of a smooth sphere of radius R. It is given a sharp impulse which imparts it a horizontal speed ν. (a) Find the normal force between the sphere and the particle just after the impulse. (b) What should be the minimum value of ν for which the particle does not slip on the sphere? (c) Assuming the velocity ν to be half the minimum calculated in part, (b) find the angle made by the radius through the particle with the vertical when it leaves the sphere.

Figure ( following ) shows a smooth track which consists of a straight inclined part of length l joining smoothly with the circular part. A particle of mass m is projected up the incline from its bottom. Find the minimum projection-speed \[\nu_0\] for which the particle reaches the top of the track.

Figure ( following ) shows a smooth track which consists of a straight inclined part of length l joining smoothly with the circular part. A particle of mass m is projected up the incline from its bottom. Assuming that the projection-speed is \[\nu_0\] and that the block does not lose contact with the track before reaching its top, find the force acting on it when it reaches the top. 

Figure ( following ) shows a smooth track which consists of a straight inclined part of length l joining smoothly with the circular part. A particle of mass m is projected up the incline from its bottom.Assuming that the projection-speed is only slightly greater than \[\nu_0\] , where will the block lose contact with the track?

A chain of length l and mass m lies on the surface of a smooth sphere of radius R > l with one end tied to the top of the sphere.  Find the gravitational potential energy of the chain with reference level at the centre of the sphere.

A chain of length l and mass m lies on the surface of a smooth sphere of radius R > l with one end tied to the top of the sphere.  Suppose the chain is released and slides down the sphere. Find the kinetic energy of the chain, when it has slid through an angle θ.

A chain of length l and mass m lies on the surface of a smooth sphere of radius R > l with one end tied to the top of the sphere.  Find the tangential acceleration \[\frac{d\nu}{dt}\] of the chain when the chain starts sliding down.

A smooth sphere of radius R is made to translate in a straight line with a constant acceleration a. A particle kept on the top of the sphere is released at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as a function of the angle θ it slides. 

The ratio stress/strain remain constant for small deformation of a metal wire. When the deformation is made larger, will this ratio increase or decrease?

When a block a mass M is suspended by a long wire of length L, the elastic potential potential energy stored in the wire is `1/2`  × stress × strain × volume. Show that it is equal to `1/2`  Mgl, where l is the extension. The loss in gravitational potential energy of the mass earth system is Mgl. Where does the remaining `1/2` Mgl energy go ? 

When the skeleton of an elephant and the skeleton of a mouse are prepared in the same size, the bones of the elephant are shown thicker than those of the mouse. Explain why the bones of an elephant are thicker than proportionate. The bones are expected to withstand the stress due to the weight of the animal.

The yield point of a typical solid is about 1%. Suppose you are lying horizontally and two persons are pulling your hands and two persons are pulling your legs along your own length. How much will be the increase in your length if the strain is 1% ? Do you think your yield point is 1% or much less than that?