Two bodies of mass $4\,kg$ and $6\,kg$ are attached to the ends of a string passing over a pulley. The $4\,kg$ mass is also attached to the ground by another string. The tension $T_1$ in this lower string is equal to ......... $N$ (Take $g = 9.8\,m/s^2$)

The maximum acceleration with which a body of mass $200 \, kg$ is lowered into a well using a rope having a breaking force of $50 \, kg$-wt is (Acceleration due to gravity $= 10 \, ms^{-2}$) (in $ \, ms^{-2}$)

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

Two blocks $A$ and $B$ of masses $1.5 \ kg$ and $0.5 \ kg$ respectively are connected by a massless inextensible string passing over a frictionless pulley as shown in the figure. Block $A$ is lifted until block $B$ touches the ground and then block $A$ is released. The initial height of block $A$ is $80 \ cm$ when block $B$ just touches the ground. The maximum height reached by block $B$ from the ground after the block $A$ falls on the ground is (in $cm$)

One end of a light string is fixed to a clamp on the ground and the other end passes over a fixed frictionless pulley as shown in the figure. It makes an angle of $30^{\circ}$ with the ground. The clamp can tolerate a vertical force of $40 \,N$. If a monkey of mass $5 \,kg$ were to climb up the rope,then the maximum acceleration in the upward direction with which it can climb safely is $\left(g=10 \,ms^{-2}\right)$ (in $\,ms^{-2}$)

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 $(g = 10 \ ms^{-2})$.