$A$ 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 ............ $N$.

For the given system,the acceleration of the system is ........... $m/s^2$.

Two blocks of masses $m$ and $2m$ are connected by a metal wire of negligible mass and having cross-sectional area $A$,passing over a smooth fixed pulley as shown in the figure. If the masses are released from rest,then the stress produced in the wire is:

$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$). If the acceleration of the system is $\frac{g}{\sqrt{2}}$,then the ratio of the masses $\frac{m_1}{m_2}$ is:

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the center $P$ (as shown in the figure). Now,the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result,the particles move towards each other on the surface. The magnitude of acceleration,when the separation between them becomes $2x$ is

The breaking stress of a wire going over a smooth pulley is $2 \times 10^9\, N/m^2$. What would be the minimum radius of the wire used if it is not to break? (Assume $g = 10\, m/s^2$)