A spring is connected to a mass m suspended from it and its time period for vertical oscillation is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is

(a)

T'= \(\sqrt{2}\)T

(b)

\(T'=\frac { T }{ \sqrt { 2 } } \)

(c)

T'=\(\sqrt{2T}\)

(d)

\(T'=\sqrt { \frac { T }{ 2 } } \)

An ideal spring of spring constant k, is suspended from the ceiling of a room and a block of mass M is fastened to its lower end. If the block is released when the spring is un-stretched, then the maximum extension in the spring is

(a)

4\(\frac { Mg }{ k } \)

(b)

\(\frac { Mg }{ k } \)

(c)

2\(\frac { Mg }{ k } \)

(d)

\(\frac { Mg }{ 2k } \)

A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will

(a)

first increase and then decrease

(b)

first decrease and then increase

(c)

increase continuously

(d)

decrease continuously

When a damped harmonic oscillator completes 100 oscillations, its amplitude is reduced to \(\frac{1}{3}\) of its initial value. What will be its amplitude when it completes 200 oscillations?

(a)

\(\frac{1}{5}\)

(b)

\(\frac{2}{3}\)

(c)

\(\frac{1}{6}\)

(d)

\(\frac{1}{9}\)

A mass of 3 kg is attached at the end of a spring moves with simple harmonic motion on a horizontal frictionless table with time period 2π and with amplitude of 2m, then the maximum fore exerted on the spring is

(a)

1.5 N

(b)

3 N

(c)

6 N

(d)

12 N