If $m_1 = 4m_2$,and the acceleration of $m_1$ is $a$,then find $a$.

Two masses $m_1$ and $m_2$ are connected by a light string passing over a smooth pulley. When set free,$m_1$ moves downwards by $3 \ m$ in $3 \ s$. The ratio of $\frac{m_1}{m_2}$ is $(g = 10 \ ms^{-2})$.

$A$ student calculates the acceleration of $m_1$ in the figure shown as $a_1 = \frac{(m_1 - m_2)g}{m_1 + m_2}$. Which assumption is not required to do this calculation?

Tension in the rope at the rigid support is ............ $N$ $\left(g=10 \,m / s ^2\right)$

Two bodies of mass $6 \ kg$ and $4 \ kg$ are tied to a string as shown in the adjoining figure. If the table and pulley are frictionless,then the acceleration of the $6 \ kg$ mass will be $........ \ ms^{-2}$ $\left(g=10 \ ms^{-2}\right)$.

$A$ pendulum bob of mass $50 \,g$ is suspended from the ceiling of an elevator. The tension in the string if the elevator goes up with uniform velocity is approximately .......... $N$.