A false balance has equal arms. An object weigh $X$ when placed in one pan and $Y$ when placed in other pan, then the weight $W$ of the object is equal to

A car accelerates on a horizontal road due to the forces exerted by

A body of mass $m_1$ exerts a force on another body of mass $m_2$. If the magnitude of acceleration of $m_2$ is $a_2$, then the magnitude of the acceleration of $m_1$ is (considering only two bodies in space)

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.

A mass of $10\,kg$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of $45^o$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ..........  $N$ $(g = 10\,ms^{-2})$ 

An uniform thick string of length $8\, m$ is resting on a horizontal frictionless surface. It is pulled by a horizontal force of $8\, N$ from one end. The tension in the string at $3\, m$ from the force applied is ........ $N$