Consider the system of $2$ pulleys as shown in figure. Both the pulleys are smooth and strings are light.

If acceleration of $m_1$ is $5 \mathrm{m} {\mathrm{s}}^{-2}$ downward, then find the value of $\frac{m_1}{m_2}$. (Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.)

Find the acceleration of the $6 \mathrm{kg}$ block in the figure. All the surfaces and pulleys are smooth. Also, the strings are inextensible and light. [Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.]

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

In the shown mass-pulley system, pulleys and string are massless. The one end of the string is pulled by the force, $F=2mg$. The acceleration of the block will be,

The system starts from rest and $A$ attains a velocity of $5 \mathrm{m} {\mathrm{s}}^{-1}$ after it has moved $5 \mathrm{m}$ towards the right. Assuming the arrangement to be frictionless everywhere and pulley and strings to be light, if the constant force $F$ applied on $A$ then find the value of $\frac{F}{15}$.

A constant force, $F=\frac{m_{1}g}{2}$ is applied on the block of mass $m_2$ as shown in figure. The string and the pulley are light and the surface of the table is smooth. Find the acceleration of $m_2$.

A dynamometer $D$ is connected with two bodies of masses, $M=6 \mathrm{kg}$ and $m=4 \mathrm{kg}$. If two forces $F=20 \mathrm{N}$ and $F=10 \mathrm{N}$ are applied on masses according to figure, then the reading of the dynamometer will be,

In the given figure, what is the reading of the spring balance?