The bob of a simple pendulum of length $200 \ cm$ is released from a horizontal position. If $10 \%$ of its initial energy is lost due to air resistance,then the speed of the bob at the mean position is (Acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $m \ s^{-1}$)

Two light strings,each of length $\ell$,are fixed at points $A$ and $B$ on a fixed horizontal rod $xy$. $A$ small bob is tied by both strings and is in equilibrium,the strings are making an angle of $45^{\circ}$ with the rod. If the bob is slightly displaced normal to the plane of the strings and released,then the period of the resulting small oscillation will be:

$A$ seconds pendulum is placed in a space laboratory orbiting round the Earth at a height $3R$ from the Earth's surface. The time period of the pendulum will be ($R =$ radius of Earth).

$A$ simple pendulum hangs from the ceiling of a car. If the car accelerates with a uniform acceleration,the frequency of the simple pendulum will

An oscillating pendulum suspended from the roof of a lift which is at rest has time period $T_1$. When the lift moves up with acceleration $a$, its time period is $T_2$. When the lift moves down with acceleration $a$, its time period is $T_3$. The relation between $T_1$, $T_2$, and $T_3$ is:

$A$ simple pendulum of length $1 \,m$ is freely suspended from the ceiling of an elevator. The time period of small oscillations as the elevator moves up with an acceleration of $2 \,m/s^2$ is (use $g=10 \,m/s^2$).