$A$ lift is going up. The total mass of the lift and the passenger is $1500\, kg$. The variation in the speed of the lift is as given in the graph. The tension in the rope pulling the lift at $t = 11\, s$ will be ............ $N$.

The pulley arrangements shown in the figure are identical, and the mass of the rope is negligible. In case $I$, the mass $m$ is lifted by attaching a mass $2m$ to the other end of the rope. In case $II$, the mass $m$ is lifted by pulling the other end of the rope with a constant downward force $F = 2mg$, where $g$ is the acceleration due to gravity. The acceleration of mass $m$ in case $I$ is

$A$ smooth massless string passes over a smooth fixed pulley. Two masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is

The system of two masses $2 \ kg$ and $3 \ kg$ as shown in the figure is released from rest. The work done on the $3 \ kg$ block by the force of gravity during the first $2 \ s$ of its motion is $\left(g=10 \ m/s^2\right)$. (in $J$)

$A$ frictionless pulley is attached to one arm of a balance and a string passed around it carries two masses $m_1$ and $m_2$. The pulley is provided with a clamp due to which $m_1$ and $m_2$ do not move with respect to each other. On removing the clamp,if the counter mass restores balance,then the acceleration of the centre of mass of the masses $m_1$ and $m_2$ will have a magnitude of?

$A$ block of mass $M$ is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force $F$. The kinetic energy of the block increases by $20\,J$ in $1\,s$.