(For simplicity in numerical calculations, take g =
10 m s-2)
>>1 Give the
magnitude and direction of the net force acting on (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.
>>.2 A pebble of mass 0.05 kg 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° with the horizontal direction? Ignore
air resistance.
>>.3 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.
>>4 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 readings on the scale in each case? (d) What would be the
reading if the lift mechanism failed and it hurtled down freely under gravity ?
>>5 Explain why (a) a horse cannot pull a cart and run in empty space, (b)
passengers are thrown forward from their seats when a speeding bus stops
suddenly,
(c) it is easier to pull a lawn mower than to push it, (d) a cricketer moves
his hands backwards while holding a catch.
>>6 A train runs along an unbanked circular
track of radius 30 m at a speed of 54 km/h. The mass of the train is 106 kg.
What provides the centripetal force required for this purpose — The engine or
the rails ? What is the angle of banking required to
prevent wearing out of the rail ?
>>7 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?
>>8 State if each
of the following statements is true or false. Give reasons for your answer. (a)
In an elastic collision of two bodies, the momentum and energy of each body is
conserved. (b) Total energy of a system is always conserved, no matter what
internal and external forces on the body are present.
(c) Work done in the motion of a body over a closed loop is zero
for every force in nature. (d) In an inelastic collision, the final kinetic
energy is always less than the initial kinetic energy of the system.
>>9 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 ?
>>10 A molecule in a gas container hits a horizontal wall with speed
200 m s–1 and angle 30° with the normal, and rebounds with the same speed. Is
momentum conserved in the
collision ? Is the collision elastic or inelastic
?
>>11 A trolley of
mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27
km/h on a frictionless track. After a while, sand starts leaking out of a hole
on the floor of the trolley at the rate of 0.05 kg s–1. What is the speed of
the trolley after the entire sand bag is empty ?