$A$ simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$,the percentage increase in the time period of the pendulum of increased length is ..... $\%$

$A$ trolley of mass $m_1$ is placed on a horizontal rigid pair of rails at the same height. $A$ mass $m_2$ is suspended from the trolley vertically by means of an ideal massless rope. The rope hangs between the rails without touching them. The trolley can move along smooth rails but cannot move in any other direction. The suspended mass is given a small oscillation and performs $SHM$ after being displaced slightly from its stable equilibrium position in two ways: first,perpendicular to the rails,and second,parallel to the rails. The ratio of the time periods of these two $SHM$s (second case to first case) is:

The metallic bob of a simple pendulum has a relative density of $5$. The time period of this pendulum is $10 \, s$. If the metallic bob is immersed in water,then the new time period becomes $5 \sqrt{x} \, s$. The value of $x$ will be.

If a simple pendulum is taken to a place where $g$ decreases by $2\%$,then the time period:

To show that a simple pendulum executes simple harmonic motion,it is necessary to assume that

$A$ simple pendulum keeps correct time at $0^{\circ}C$. At $25^{\circ}C$,it loses $12.5 \, s$ in a day. What is the coefficient of linear expansion of the metal of the pendulum?