Question

Which of the following has maximum momentum:
1. A 150 kg car moving at 0.3 m/s
2. A 10 gm mass moving at 4000 cm/s
3. A 400 gm weight moving with kinetic energy of 2×10^-5 J
4. A 10 gm mass after falling 2 km

Answer 1

Correct Answer - Option 1 : A 150 kg car moving at 0.3 m/s

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

CALCULATION:

When m = 150 kg and v = 0.3 m/s,

⇒ P = mv

⇒ P = 150 × 0.3

⇒ P = 45 kg-m/s

When m = 10 gm and v = 4000 cm/s,

\(⇒ m =\frac{10}{1000}\,kg\)

​\(⇒ m =\frac{1}{100}\,kg\)​

\(⇒ v=\frac{4000}{100}\,m/s\)

⇒ v = 40 m/s

⇒ P = mv

\(⇒ P =\frac{1}{100}×40\,kg-m/s\)

⇒ P = 0.4 kg-m/s

When m = 400 gm and KE = 2×10-5 J,

\(⇒ m =\frac{400}{1000}\,kg\)

⇒ m = 0.4 kg

We know that,

\(⇒ P=\sqrt{2× KE× m}\)

\(⇒ P=\sqrt{2× 2×10^{-5}× 0.4}\)

⇒ P = 4×10^-3 kg-m/s

When m = 10 gm, h = 2 km and a = g = 9.8 m/s²,

⇒ h = 2000 m

By third equation of motion,

⇒ v² = u² + 2gh

⇒ v² = 0² + 2 × 9.8 × 2000

⇒ v = 198 m/s

⇒ P = mv

⇒ P = 0.01 × 198

⇒ P = 1.98 kg-m/s

• Hence, option 1 is correct.