$A$ mass $m$ is tied to one end of a spring and whirled in a horizontal circle with constant angular velocity. The elongation in the spring is $1 \ cm$. If the angular speed is doubled,the elongation in the spring is $6 \ cm$. The original length of the spring is (in $cm$)

Five persons $A, B, C, D$ and $E$ are pulling a cart of mass $100 \, kg$ on a smooth surface and the cart is moving with an acceleration of $3 \, m/s^2$ in the east direction. When person $A$ stops pulling,it moves with an acceleration of $1 \, m/s^2$ in the west direction. When person $B$ stops pulling,it moves with an acceleration of $24 \, m/s^2$ in the north direction. The magnitude of the acceleration of the cart when only $A$ and $B$ pull the cart,keeping their directions the same as the original directions,is ............ $m/s^2$.

$A$ person of mass $60\, kg$ is inside a lift of mass $940\, kg$ and presses the button on the control panel. The lift starts moving upwards with an acceleration of $1.0\, m/s^2$. If $g = 10\, m/s^2$,the tension in the supporting cable is .......... $N$.

$A$ block of mass $m$ is moving with a constant acceleration $a$ on a rough plane. If the coefficient of friction between the block and the ground is $\mu$,the power delivered by the external agent after a time $t$ from the beginning is equal to:

Two blocks of equal masses are connected with a massless spring of spring constant $k = 2500 \,N/m$ and natural length $10 \,cm$, resting on a frictionless horizontal plane. If a constant horizontal force $F = 10 \,N$ is applied as shown in the figure, find the maximum distance between the blocks. (in $cm$)

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. When a person walks on a rough surface,the direction of the frictional force exerted by the surface on the person is in the same direction as his motion.
$B$. When a cycle is in motion,the force of friction exerted by the ground on the front wheel is in the backward direction.