A simple pendulum is suspended from the top of the roof of a lift. What happens to its Time period if; (a) The lift accelerates upwards with an acceleration \(a\)? (b) The lift accelerates downward with an acceleration \(a\)? (c) The lift moves upwards and downwards with constant velocity? and if (d)The cables of the lift are cut and lift begins to fall freely?
A second’s pendulum is taken in carriage. Find: the period of oscillation when the carriage moves with an acceleration of \(4\frac{m}{s^{2}}\); (i) Vertically Upwards. (ii) Vertically downwards. and (iii) In horizontal direction.
Ans:(i) \(T_{1}=1.66Sec\) (ii) \(T_{2}=2.72Sec\) and (iii) \(T_{3}=1.91Sec\).
Two pendulum of lengths \( 100cm \) and \(110.25cm\) starts oscillating in phase. After how many oscillations will they again be in same phase?
Ans: \(\nu=20\).
A pendulum clock normally shows the correct time. On an extremely cold day, its length decreases by \(0.3\%\). Compute the error in time per day?
Ans: \(\Delta T=129.6Sec.\).
If the length of a second’s pendulum is increased by \(1\%\), how many seconds will it lose in a day?
Ans: \(432Sec\).
The bottom of the dip on a road has a radius of curvature \(R\). A rickshaw of mass \(M\) left a little away from the bottom oscillates about the dip. Deduce an expression for the period of oscillation.
Ans: \(T=2\pi\sqrt{\frac{R}{g}}\).
A test tube weighing \(10g\) and external diameter \(2cm\) is floated vertically in water by placing \(10g\) of mercury at its bottom. The tube is then depressed in water a little and then released. Find: the time of oscillations. Take: \(g=10\frac{m}{s^{2}}\).
Ans: \(T=0.5Sec\).
A sphere is hung with a wire. \(45^{o}\) rotation of the sphere about the wire generates a restoring torque of \(6.0N-m\). If the moment of inertia of the sphere is \(0.080kg.m^{2}\) then deduce the frequency of the angular oscillations.
Ans: \(\nu=\frac{1}{2\pi}\sqrt{\frac{C}{I}}\).
A vertical U-tube of uniform cross-section contains water up to height of \(2.45cm\). If, the water in one side is depressed and the released, its up and down motion in tube is simple harmonic. Calculate: the Time period of the oscillation.
Ans: \(T=0.314Sec\).
A cylindrical wooden block having cross-sectional area of \(25.00cm^{2}\) and mass \(250g\) is floating over water with an extra weight of \(50g\) attached at its bottom. The cylinder floats vertically. From the equilibrium state it is slightly depressed and released. If, the specific gravity of the wood is \(0.30\) and \(g=10\frac{m}{s^{2}}\). Then, what is the frequency of the block’s oscillation.
