$A$ body of mass $10 \, kg$ at rest is acted upon simultaneously by two forces $4 \, N$ and $3 \, N$ at right angles to each other. The kinetic energy of the body at the end of $10 \, s$ is .............. $J$.

$A$ lorry and a car moving with the same $K.E.$ are brought to rest by applying the same retarding force,then

$A$ particle of mass $m$ is at rest in a train moving with constant velocity with respect to the ground. Now,the particle is accelerated by a constant force $F_0$ acting along the direction of motion of the train for time $t_0$. $A$ girl in the train and a boy on the ground measure the work done by this force. Which of the following are $INCORRECT$?

$A$ block of mass $1.9\, kg$ is at rest at the edge of a table of height $1\, m$. $A$ bullet of mass $0.1\, kg$ collides with the block and sticks to it. If the velocity of the bullet is $20\, m/s$ in the horizontal direction just before the collision,then the kinetic energy just before the combined system strikes the floor is $....J$. (Take $g = 10\, m/s^2$. Assume there is no rotational motion and loss of energy after the collision is negligible.)

$A$ person of mass $60 \, kg$ wants to lose $5 \, kg$ by going up and down a $10 \, m$ high stairs. Assume he burns twice as much fat while going up than coming down. If $1 \, kg$ of fat is burnt on expending $7000 \, kcal$,how many times must he go up and down to reduce his weight by $5 \, kg$?

$A$ bullet of $10\, \text{g}$, moving with velocity $v$, collides head-on with the stationary bob of a pendulum and recoils with velocity $100\, \text{m/s}$. The length of the pendulum is $0.5\, \text{m}$ and the mass of the bob is $1\, \text{kg}$. The minimum value of $v$ in $\text{m/s}$ so that the pendulum completes a vertical circle is: (Assume the string to be inextensible and $g=10\, \text{m/s}^2$)