The length of the seconds pendulum is $1 \,m$ on Earth. If the mass and diameter of a planet are $1.5$ times that of the Earth, the length of the seconds pendulum on the planet will be nearly (in $\,m$)

Which vector in the figures best represents the acceleration of a pendulum mass at the intermediate point in its swing?

$A$ simple pendulum oscillates in a vertical plane. When it passes through the mean position,the tension in the string is $3$ times the weight of the pendulum bob. What is the maximum displacement of the pendulum string with respect to the vertical in degrees?

$A$ 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?

If the length of the oscillating simple pendulum is made $\frac{1}{3}$ times the original, keeping the amplitude the same, then the increase in its total energy at a place will be: (in $\times$)

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$,is given by