Question

If the velocity of a body of mass 10 kg is changing from 20 m/sec to 30 m/sec in 0.6 sec. Then the impulse on the body is:
1. 200 kg-m/sec
2. 100 kg-m/sec
3. 300 kg-m/sec
4. 400 kg-m/sec

Answer 1

Correct Answer - Option 2 : 100 kg-m/sec

CONCEPT:

Linear Momentum:

• The linear momentum of a body is the quantity of motion contained in the body.
• It is measured in terms of the force required to stop the body in unit time.
• It is also measured as the product of the mass of the body and its velocity i.e.,

⇒ Momentum (P) = mass (m) × velocity (v)

⇒ P = mv

Impulse:

• When a large force is acting on a body for a short period of time to produce a finite change in its momentum is called impulsive force.
• The impulse is given as,

⇒ I = F×dt

• Impulse is also equal to the change in momentum.

EXPLANATION:

Given m = 10 kg, v₁ = 20 m/sec, v2 = 30 m/sec, and dt = 0.6 sec

• The momentum is given as,

⇒ P = mv     -----(1)

• So initial momentum is given as,

⇒ P₁ = mv₁

⇒ P1 = 10 × 20 

⇒ P1 = 200 kg-m/sec     -----(2)

• And final momentum is given as,

⇒ P2 = mv2

⇒ P2 = 10 × 30

⇒ P2 = 300 kg-m/sec     -----(3)

By equation 2 and equation 3 the change in momentum is given as,

⇒ ΔP = P₂ - P₁

⇒ ΔP = 300 - 200

⇒ ΔP = 100 kg-m/sec

• We know that the impulse is equal to the change in momentum,

⇒ I = ΔP

⇒ I = 100 kg-m/sec

• Hence, option 2 is correct.