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

Three equal weights $A, B$ and $C$ of mass $2\, kg$ each are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in the string connecting weights $B$ and $C$ is ........... $N$.

$A$ loop of light inextensible string passes over smooth small pulleys $A$ and $B$. Two masses $m$ and $M$ are attached to the points $O$ and $C$ respectively. The condition that $m$ and $M$ will cross each other (given $AB = 2l$ and $AC = BC = \eta l$) is:

$A$ mass of $1 \ kg$ is suspended by a string $A$. Another string $C$ is connected to its lower end (see figure). If the string $C$ is stretched slowly,then

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

$A$ 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 ............ $^o$.