If $m_1 = 4m_2$ and the acceleration of $m_1$ is $a$,find the tension $T$ in the string.

For the system shown in the figure,the pulleys are light and frictionless. The tension in the string will be

Two blocks of mass $M$ and $m$ are kept on a trolley of mass $M_0$ as shown in the figure. All surfaces are smooth. Select the correct statement.

Two masses $M_{1}$ and $M_{2}$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_{2}$ is twice that of $M_{1}$,the acceleration of the system is $a_{1}$. When the mass $M_{2}$ is thrice that of $M_{1}$,the acceleration of the system is $a_{2}$. The ratio $\frac{a_{1}}{a_{2}}$ will be:

$A$ boy is hanging from the branch of a tree as shown. For the tension in his arms to be maximum,the angle between his arms must be ............ $^o$.

Three blocks of masses $m_1=4 \, kg$, $m_2=2 \, kg$, and $m_3=4 \, kg$ are connected with ideal strings passing over a smooth, massless pulley as shown in the figure. The acceleration of the blocks will be ......... $m/s^2$ $(g=10 \, m/s^2)$.