PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

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?

A steel blade placed gently on the surface of water floats on it. If the same blade is kept well inside the water, it sinks. Explain.

When some wax is rubbed on a cloth, it becomes waterproof. Explain.

All the surfaces shown in figure are frictionless. The mass of the care is M, that of the block is m and the spring has spring constant k. Initially the car and the block are at rest and the spring is stretched through a length x₀ when the system is released. (a) Find the amplitudes of the simple harmonic motion of the block and of the care as seen from the road. (b) Find the time period(s) of the two simple harmonic motions.

A pendulum having time period equal to two seconds is called a seconds pendulum. Those used in pendulum clocks are of this type. Find the length of a second pendulum at a place where g = π² m/s².

The angle made by the string of a simple pendulum with the vertical depends on time as \[\theta = \frac{\pi}{90}  \sin  \left[ \left( \pi  s^{- 1} \right)t \right]\] .Find the length of the pendulum if g = π² m².

The pendulum of a certain clock has time period 2.04 s. How fast or slow does the clock run during 24 hours?

A pendulum clock giving correct time at a place where g = 9.800 m/s² is taken to another place where it loses 24 seconds during 24 hours. Find the value of g at this new place.

A simple pendulum is constructed by hanging a heavy ball by a 5.0 m long string. It undergoes small oscillations. (a) How many oscillations does it make per second? (b) What will be the frequency if the system is taken on the moon where acceleration due to gravitation of the moon is 1.67 m/s²?

A rope 1 cm in diameter breaks if the tension in it exceeds 500 N. The maximum tension that may be given to a similar rope of diameter 2 cm is

The breaking stress of a wire depends on

A wire can sustain the weight of 20 kg before breaking. If the wire is cut into two equal parts, each part can sustain a weight of 

A small block oscillates back and forth on a smooth concave surface of radius R ib Figure . Find the time period of small oscillation.

A small block oscillates back and forth on a smooth concave surface of radius R in Figure. Find the time period of small oscillation.

A heave uniform rod is hanging vertically form a fixed support. It is stretched by its won weight. The diameter of the rod is