Q. A bob of mass $0.1kg$ hung from the ceiling of a room by a string $2m$ long is set into oscillation. The speed of the bob at its mean position is $1m{s}^{-1}$.What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.

Q. (a) A drop of rain falling down with a constant speed.
(b) A cork of mass $10$ $g$ floating on water.
(c) A kite skillfully held stationary in the sky.
(d) A car moving with a constant velocity of $30$ $km/h$ on a rough road.
(e) A high-speed electron in space far from all material objects, and free of electric and magnetic fields.

Q. A man of mass $70$ $kg$ stands on a weighing scale in a lift which is moving.
(a) Upwards with a uniform speed of $10$ $m{s}^{-1}$.
(b) Downwards with a uniform acceleration of $5$ $m{s}^{-2}$.
(c) Upwards with a uniform acceleration of $5$ $m{s}^{-2}$.
What would be the reading on the scale in each case?
(d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

Q. A body of mass $5kg$ is acted upon by two perpendicular forces $8N$ and $6N$.Give the magnitude and direction of the acceleration of the body.

Q. A constant force acting on a body of mass $3.0kg$ changes its speed from $2.0m$ $s^{-1}$ to $3.5m$ $s^{-1}$ in $25s$. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force?

Q. A constant retarding force of $50$ $N$ is applied to a body of mass $20$ $kg$ moving initially with a speed of $15$ $m{s}^{-1}$. How long does the body take to stop?

Q. One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$ the net force on the particle ( directed towards the centre ) is :

1. $T$
2. $T+\frac{m{v}^2}{l}$
3. $T-\frac{m{v}^2}{l}$
4. $0$

Q. Figure shows the position-time graph of a particle of mass $4kg$. What is the (a) force on the particle for $t<0,t>4s,0<t<4s$ (b) impulse at t = 0 and t = 4 s? (Consider one-dimensional motion only).

Q. A pebble of mass $0.05kg$ 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.

Q. The driver of a three-wheeler moving with a speed of $36$ $km/h$ sees a child standing in the middle of the road and brings his vehicle to rest in $4.0$ $s$ just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is $400$ $kg$ and the mass of the driver is $65$ $kg$.

Q. Give the magnitude and direction of the net force acting on a stone of mass $0.1$ $kg$.(a) Just after it is dropped from the window of a stationary train.(b) Just after it is dropped from the window of a train running at a constant velocity of $36$ $km/h$.(c) Just after it is dropped from the window of a train accelerating with $1$ $m{s}^{-2}$.(d) Lying on the floor of a train which is accelerating with $1$ $m{s}^{-2}$, the stone being at rest relative to the train. Neglect air resistance throughout

Q. A batsman deflects a ball by an angle of ${90}^o$ without changing its initial speed, which is equal to $54km/hr$. What is the impulse imparted to the ball? (Mass of the ball is $0.15kg$).

Q. A body of mass $0.40kg$ moving initially with a constant speed of $10m{s}^{-1}$ to the north is subject to a constant force of $8.0N$ directed towards the south for $30s$. Take the instant the force is applied to be $t=0$, the position of the body at that time to be $x=0$, and predict its position at $t=5s,25s,100s$.

Q. A rocket with a lift-off mass $20,000kg$ is blasted upwards with an initial acceleration of $5.0m{s}^{-2}$. Calculate the initial thrust (force) of the blast.

Q. A truck starts from rest and accelerates uniformly at $2.0m{s}^{-2}$. At $t=10s$, a stone is dropped by a person standing on the top of the truck ($6m$ high from the ground). What are the (a) velocity, and (b) acceleration of the stone at $t=11s$ ? (Neglect air resistance.)

Q. Two bodies of masses $10$ $kg$ and $20$ $kg$ respectively, kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force $F$ $=$ $600$ $N$ is applied to(i) A (ii) B along the direction of string. What is the tension in the string in each case?

Q. Two billiard balls each of mass $0.05kg$ moving in opposite directions with speed $6m{s}^{-1}$collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?

Q. A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.

Q. A shell of mass $0.020kg$ is fired by a gun of mass $100kg$. If the muzzle speed of the shell is $80m/s$, what is the recoil speed of the gun?

Q. Two masses $8$ $kg$ and $12$ $kg$ are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.