PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

A disc of radius 10 cm is rotating about its axis at an angular speed of 20 rad/s. Find the linear speed of a point on the rim.

A disc of radius 10 cm is rotating about its axis at an angular speed of 20 rad/s. Find the linear speed of the middle point of a radius.

A block hangs from a string wrapped on a disc of radius 20 cm free to rotate about its axis which is fixed in a horizontal position. If the angular speed of the disc is 10 rad/s at some instant, with what speed is the block going down at that instant?

The maximum speed and acceleration of a particle executing simple harmonic motion are 10 cm/s and 50 cm/s². Find the position(s) of the particle when the speed is 8 cm/s.

A particle having mass 10 g oscillates according to the equation x = (2.0 cm) sin [(100 s⁻¹)t + π/6]. Find (a) the amplitude, the time period and the spring constant. (c) the position, the velocity and the acceleration at t = 0.

Consider a particle moving in simple harmonic motion according to the equation x = 2.0 cos (50 πt + tan⁻¹ 0.75) where x is in centimetre and t in second. The motion is started at t = 0. (a) When does the particle come to rest for the first time? (b) When does he acceleration have its maximum magnitude for the first time? (c) When does the particle come to rest for the second time ?

The pendulum of a clock is replaced by a spring-mass system with the spring having spring constant 0.1 N/m. What mass should be attached to the spring?

A block suspended from a vertical spring is in equilibrium. Show that the extension of the spring equals the length of an equivalent simple pendulum, i.e., a pendulum having frequency same as that of the block.

A block of mass 0.5 kg hanging from a vertical spring executes simple harmonic motion of amplitude 0.1 m and time period 0.314 s. Find the maximum force exerted by the spring on the block.

A body of mass 2 kg suspended through a vertical spring executes simple harmonic motion of period 4 s. If the oscillations are stopped and the body hangs in equilibrium find the potential energy stored in the spring.

The block of mass m₁ shown in figure is fastened to the spring and the block of mass m₂ is placed against it. (a) Find the compression of the spring in the equilibrium position. (b) The blocks are pushed a further distance (2/k) (m₁ + m₂)g sin θ against the spring and released. Find the position where the two blocks separate. (c) What is the common speed of blocks at the time of separation?

In following figure k = 100 N/m M = 1 kg and F = 10 N. 

1. Find the compression of the spring in the equilibrium position. 
2. A sharp blow by some external agent imparts a speed of 2 m/s to the block towards left. Find the sum of the potential energy of the spring and the kinetic energy of the block at this instant. 
3. Find the time period of the resulting simple harmonic motion. 
4. Find the amplitude. 
5. Write the potential energy of the spring when the block is at the left extreme. 
6. Write the potential energy of the spring when the block is at the right extreme.
   The answer of b, e and f are different. Explain why this does not violate the principle of conservation of energy.
   

The spring shown in figure is unstretched when a man starts pulling on the cord. The mass of the block is M. If the man exerts a constant force F, find (a) the amplitude and the time period of the motion of the block, (b) the energy stored in the spring when the block passes through the equilibrium position and (c) the kinetic energy of the block at this position.

Repeat the previous exercise if the angle between each pair of springs is 120° initially.

The springs shown in the figure are all unstretched in the beginning when a man starts pulling the block. The man exerts a constant force F on the block. Find the amplitude and the frequency of the motion of the block.

Find the elastic potential energy stored in each spring shown in figure, when the block is in equilibrium. Also find the time period of vertical oscillation of the block.

Solve the previous problem if the pulley has a moment of inertia I about its axis and the string does not slip over it.

Consider the situation shown in figure . Show that if the blocks are displaced slightly in opposite direction and released, they will execute simple harmonic motion. Calculate the time period.

A rectangle plate of sides a and b is suspended from a ceiling by two parallel string of length L each in Figure . The separation between the string is d. The plate is displaced slightly in its plane keeping the strings tight. Show that it will execute simple harmonic motion. Find the time period.