$A$ 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 up to $2 \ m$ height further,find the magnitude of the force $F$ in $N$. (Consider $g = 10 \ m/s^2$)

State whether the following statements are true or false:
$(a)$ Power is the vector product of force and velocity.
$(b)$ $1\,kg\,m = 9.8\,J$
$(c)$ When a teacher rubs a blackboard with a duster,they do no work.
$(d)$ Kinetic energy can be negative.

Three blocks $A, B$ and $C$ are kept as shown in the figure. The coefficient of friction between $A$ and $B$ is $0.2$,$B$ and $C$ is $0.1$,and $C$ and the ground is $0.0$. The masses of $A, B$ and $C$ are $3\, kg, 2\, kg$ and $1\, kg$ respectively. $A$ is given a horizontal velocity of $10\, m/s$. Blocks $A, B$ and $C$ always remain in contact and move together as a single system. The total work done by friction will be ........ $J$.

$A$ simple pendulum of length $1 \ m$ has a bob of mass $1 \ kg$. $A$ bullet of mass $10^{-2} \ kg$ is fired into the bob with a speed of $2 \times 10^2 \ m/s$. The bullet gets embedded in the bob. Find the height $h$ to which the bob rises before it swings back. (in $m$)

$A$ mass of $2.9 \ kg$ is suspended from a string of length $50 \ cm$ and is at rest. Another body of mass $100 \ g$,which is moving horizontally with a velocity of $150 \ m/s$,strikes and sticks to it. Subsequently,when the string makes an angle of $60^{\circ}$ with the vertical,the tension in the string is $(g = 10 \ m/s^2)$. (in $N$)

Two bodies of masses $m$ and $2m$ are attached to the two ends of an ideal spring. The spring is compressed. The total energy stored in the spring is $60 \ J$. If the spring is released,then: