Two bodies A and B of masses 5 kg and 10 kg in contact with each other rest on a table against a rigid wall (Fig. 5.21). The coefficient of friction between the bodies and the table is 0.15. A force of 200 N is applied horizontally to A. What are (a) the reaction of the partition

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

A man of mass 70 kg stands on a weighing scale in a lift which is moving (d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity ?

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

Give the magnitude and direction of the net force acting on (d) a car moving with a constant velocity of 30 km/h on a rough road,

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.

A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed ?

A helicopter of mass 1000 kg rises with a vertical acceleration of $15 m s^{-2}$. The crew and the passengers weigh 300 kg. Give the magnitude and direction of the (c) force on the helicopter due to the surrounding air.

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.

A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is $80 m s^{-1}$, what is the recoil speed of the gun ?

Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (c) just after it is dropped from the window of a train accelerating with $1 m s^{-2}$,

Explain why (c) it is easier to pull a lawn mower than to push it,

A stream of water flowing horizontally with a speed of $15 m s^{-1}$ gushes out of a tube of cross-sectional area $10^{-2} m^2$, and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound ?

You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘death-well’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m ?

Ten one-rupee coins are put on top of each other on a table. Each coin has a mass m. Give the magnitude and direction of (a) the force on the 7th coin (counted from the bottom) due to all the coins on its top,

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

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

A disc revolves with a speed of $33\frac{1}{3}$ rev/min, and has a radius of 15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of the record. If the co-efficient of friction between the coins and the record is 0.15, which of the coins will revolve with the record ?

Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h,

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