Question

1
6. Two balls A and B of masses m and 2m are in
motion with velocities 2v and v respectively.
Compare
(i) their inertia, (ii) their momentum, and (iii) the
force needed to stop them in the same time.​

Answer 1

Answer:

i) 1:2

(ii) 1 :1

Explanation:

(i) Inertia depends on mass, and since the mass of the two balls are m and 2m, So the ratio of inertia of the balls 1:2

(ii)Momentum , p=mv

So, as per momentum equation, it depends on both mass and velocity.

So, their ratio =m×2v:2m×v=1:1

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///\DI

Answer 2

Solution :

As per the given data ,

• Mass of A = m
• Mass of B = 2m
• Velocity of A = 2v
• Velocity of B = v

(1) Inertia

Inertia of the body depends only upon it's mass

Hence ,

The inertia of both the balls are in the ratio of 1 :2 .

(2) Momentum

A per the formula ,

⇒ P = mv

here ,

• P = momentum
• m = mass
• v = velocity

⇒ P = m x 2v = 2 mv

Similarly ,

⇒ P' = 2m x v = 2mv

Ratio of  momentum

⇒ P/ P' = 2mv/2mv

⇒ P/P' =  1

The momentum of both the balls are in the ratio 1 :1  .

(3) Force

As per the formula ,

⇒ F = ΔP / t

⇒ F = 0 - 2 mv / t [ as the ball stops ]

⇒ F = - 2mv / t

Similarly ,

⇒ F' = - 2mv / t

The forces of both the balls are in the ratio 1 :1