A ball of mass $0.2\ kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2\ m$ while applying the force and the ball goes upto $2\ m$ height further, find the  magnitude of the force .......... $N$ .(consider $g = 10\; m/s^2$)

A uniform cable of mass $‘M’$ and length $‘L’$ is placed on a horizontal surface such that its ${\left( {\frac{1}{n}} \right)^{th}}$  part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:

$(a)$ work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.

$(b)$ work done by gravitational force in the above case,

$(c)$ work done by friction on a body sliding down an inclined plane,

$(d)$ work done by an applied force on a body moving on a rough horizontal plane with uniform velocity,

$(e)$ work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

A spherical ball of mass $20\, kg$ is stationary at the top of a hill of height $100 \,m$. It slides down a smooth surface to the ground, then climbs up another hill of height $30 \,m$ and finally slides down to a horizontal base at a height of $20 \,m$ above the ground. The velocity attained by the ball is ............... $\mathrm{m} / \mathrm{s}$

A mass of $M\ kg$ is suspended by a weightless string. The horizontal force that is displace it until the string makes an angle of $45^o $ with the initial vertical direction is

Power on $a$ mass is $P = (3t^2 -2t + 1)$ watt change in kinetic energy in $t = 2sec$ to $t = 4sec$ is :- .................... $\mathrm{J}$