Laws of Motion

• Question 541

## A shell of mass 200 g is ejected from a gun of mass 4 g by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is 100 ms-1 80 ms-1 40 ms-1 120 ms-1

Solution

A.

100 ms-1

In the given problem conservation of linear momentum and energy hold good.
Conservation of momentum yields.
m1v1 + m2v2 = 0
4v1 + 0.2 v2  = 0
Conservation of energy yields

Question 542

## Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be Mv newton 2 Mv newton Mv/2 Newton zero

Solution

A.

Mv newton

Force required,

as velocity v is constant, hence
F= Mv newton

Question 543

## A block B is pushed momentarily along a horizontal surface with an initial velocity v. if μ is the coefficient of sliding friction between B  and the surface, block B will come to rest after a time: v/gμ gμ/v g/v v/g

Solution

A.

v/gμ

Block B will come to rest, if force applied to it will vanish due to frictional force acting between block B and surface, ie,
force applied = frictional force
i.e., μmg = ma
μmg = m (v/t)
t =v/μg

Question 544

## 300 J of work is done in sliding a 2 kg block up an inclined plane of height 10 m. Taking =10 m/s2, work done against friction is 200 J 100 J Zero 1000 J

Solution

B.

100 J

Net work done in sliding a body up to a height h on inclined plane
= Work done against gravitational force + Work done against frictional force