Two masses $m$ and $M$ are attached to the strings as shown in the figure. If the system is in equilibrium, then
$\cot \theta=1+\frac{2 m}{M}$
$\tan \theta=1+\frac{2 M}{m}$
$\tan \theta=1+\frac{2 m}{M}$
$\cot \theta=1+\frac{2 M }{ m }$
A uniform sphere of weight $W$ and radius $3\,m$ is being held by a string of length $2\,m$ , attached to a frictionless wall as shown in the figure. The tension in the string will be
A smooth cylinder of mass $m$ and radius $R$ is resting on two corner edges $A$ and $B$ as shown in fig. The relation between normal reaction at the edges $A$ and $B$ is
A pebble of mass $0.05\; kg$ is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble,
$(a)$ during its upward motion,
$(b)$ during its downward motion,
$(c)$ at the highest point where it is momentarily at rest.
Do your answers change if the pebble was thrown at an angle of $45^o$ with the horizontal direction? Ignore air resistance.
Adjoining figure shows a force of $40\, N$ acting at $30^o$ to the horizontal on a body of mass $5 \,kg$ resting on a smooth horizontal surface. Assuming that the acceleration of free-fall is $10\, ms^{-2}$, which of the following statements is (are) correct?
$[1]$ The horizontal force acting on the body is $20\, N$
$[2]$ The weight of the $5\, kg$ mass acts vertically downwards
$[3]$ The net vertical force acting on the body is $30\, N$
A mass of $5\, kg$ is suspended by a rope of length $2\,m$ from a ceiling. A force of $50\,N$ in the horizontal direction is applied at the mid-point of the rope. The angle made by the rope with the vertical, in equilibrium is ........ $^o$