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In an explosion a body breaks up into two pieces of unequal masses. In this

Both parts will have numerically equal momentum

Lighter part will have more momentum

Heavier part will have more momentum

Both parts will have equal kinetic energy

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Explanation

Both part will have numerically equal momentum and lighter part will have more velocity.

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Two bodies of masses m₁ and m₂ have equal kinetic energies. If p₁ and p₂ are their respective momentum, then ratio p₁ : p₂ is equal to

$m_{1} : m_{2}$

$m_{2} : m_{1}$

$\sqrt{m_{1}} : \sqrt{m_{2}}$

$m_{1}^{2} : m_{2}^{2}$

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Explanation

$P = \sqrt{2 m E}$

∴ $P \propto \sqrt{m}$ $(if E = const.)$

∴ $\frac{P_{1}}{P_{2}} = \sqrt{\frac{m_{1}}{m_{2}}}$

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A light and a heavy body have equal momenta. Which one has greater K.E

The light body

The heavy body

The K.E. are equal

Data is incomplete

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Explanation

$E = \frac{P^{2}}{2 m}$ if P = constant then $E \propto \frac{1}{m}$

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If the momentum of a body is increased n times, its kinetic energy increases-

n times

2n times

$\sqrt{n}$ times

n² times

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Explanation

$E = \frac{P^{2}}{2 m}$ ∴ $E \propto P^{2}$

i.e. if P is increased n times then E will increase n² times.

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A bomb of 12 kg explodes into two pieces of masses 4 kg and 8 kg. The velocity of 8kg mass is 6 m/sec. The kinetic energy of the other mass is

48 J

32 J

24 J

288 J

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Two masses of 1 gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

4 : 1

$\sqrt{2} : 1$

1 : 2

1 : 16

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Explanation

$P = \sqrt{2 m E} .$ If E are same then $P \propto \sqrt{m}$

⇒ $\frac{P_{1}}{P_{2}} = \sqrt{\frac{m_{1}}{m_{2}}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$

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If the K.E. of a body is increased by 300%, its momentum will increase by

100%

150%

$\sqrt{300} %$

175%

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Explanation

Let initial kinetic energy, $E_{1} = E$

Final kinetic energy, $E_{2} = E + 300 %$ of E = 4E

As $P \propto \sqrt{E}$ ⇒ $\frac{P_{2}}{P_{1}} = \sqrt{\frac{E_{2}}{E_{1}}} = \sqrt{\frac{4 E}{E}} = 2$ ⇒ $P_{2} = 2 P_{1}$

⇒ $P_{2} = P_{1} + 100 %$ of $P_{1}$

i.e. Momentum will increase by 100%.

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A light and a heavy body have equal kinetic energy. Which one has a greater momentum ?

The light body

The heavy body

Both have equal momentum

It is not possible to say anything without additional information

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Explanation

$P = \sqrt{2 m E}$ if E are equal then $P \propto \sqrt{m}$

i.e. heavier body will possess greater momentum.

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If the K.E. of a particle is doubled, then its momentum will

Remain unchanged

Be doubled

Be quadrupled

Increase $\sqrt{2}$ times

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Explanation

$P = \sqrt{2 m E}$ ∴ $P \propto \sqrt{E}$

i.e. if kinetic energy of a particle is doubled the its momentum will becomes $\sqrt{2}$ times.

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Two bodies of different masses m₁ and m₂ have equal momenta. Their kinetic energies E₁ and E₂ are in the ratio

$\sqrt{m_{1}} : \sqrt{m_{2}}$

$m_{1} : m_{2}$

$m_{2} : m_{1}$

$m_{1}^{2} : m_{2}^{2}$

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Explanation

$E = \frac{P^{2}}{2 m}$ if bodies possess equal linear momenta then

$E \propto \frac{1}{m}$ i.e. $\frac{E_{1}}{E_{2}} = \frac{m_{2}}{m_{1}}$

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