An automobile vehicle has a mass of 1500 kg. What must be the force between the vehicle and road if the vehicle is to be stopped with a negative acceleration of `1.7 m s^-2`?

The masses of two bodies are m_1 and m_2 the distance between them is d. What is the gravitational force between them?

Two persons manage to push a motorcar of mass 1200 kg at a uniform velocity along a level road, the same motorcar can be pushed by three persons to produce an acceleration of 0.2 m s^-2 . With what force does each person push the motorcar? (Assume that all persons push the motorcar with the same muscular effort.)

A flywheel of mass 25kg has a radius of 0.2 m. What force should be applied to the rim so that it acquires an angular acceleration of 5 rads^(-2) ?

Figure 5.18 shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s^2 . What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg.)

A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey (a) climbs up with an acceleration of 6 m s^2 (b) climbs down with an acceleration of 4 m s^2 (c) climbs up with a uniform speed of 5 m s^1 (d) falls down the rope nearly freely under gravity? (Ignore the mass of the rope).

A scooter of mass 120 kg is moving with a uniform velocity of 108 km/h. Calculate the force required to stop the vehicle in 10 sec.

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, upwards with a uniform acceleration of 5 m s-^1z. What would be the readings on the scale in each case? What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

Find the force needed to produce an acceleration of 6 m/s2 in a ball of mass 4kg.

Two bodies whose masses are m_1 = 50 kg and m_2 150g are tight by a string and placed in a horizontal surface. When m_1 is pulled by a force F and acceleration of 5ms^-2 is produced in both the bodies. Calculate the value of F and tension in the strong.

A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is 10 m s-^1 ?