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PHXI06:WORK ENERGY AND POWER

355421 Four particles $A, B, C, D$ of mass $\frac{m}{2}, m, 2 m, 4 m$ , have same momentum, respectively. The particle with maximum kinetic energy is

1

C

2

A

3

D

4

B

Explanation:

$K E = \frac{p^{2}}{2 m}$
For same momentum $(p), K E \propto \frac{1}{m}$
Therefore, the lightest particle will possess maximum kinetic energy.
$∴$ A possess maximum kinetic energy.
So, correct option is (2).

JEE - 2024

PHXI06:WORK ENERGY AND POWER

355422 Two bodies are having kinetic energies in the ratio $16 : 9$ . If they have same linear momentum, the ratio of their masses respectively is

1

4 : 3

2

16 : 9

3

3 : 4

4

9 : 16

Explanation:

Kinetic energy of a body is given by
$K = \frac{p^{2}}{2 m}$
where, $p =$ momentum, $m =$ mass
$\Rightarrow \frac{K_{1}}{K_{2}} = {(\frac{p_{1}}{p_{2}})}^{2} (\frac{m_{2}}{m_{1}})$
Given, $p_{1} = p_{2}$
$\Rightarrow \frac{K_{1}}{K_{2}} = \frac{m_{2}}{m_{1}}$
$\Rightarrow \frac{m_{1}}{m_{2}} = \frac{K_{2}}{K_{1}} = \frac{9}{16}$

JEE - 2023

PHXI06:WORK ENERGY AND POWER

355423 Statement A :
A light body and a heavy body have same momentum. Then they also have same kinetic energy.
Statement B :
Kinetic energy does not depend on mass of the body

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

Explanation:

$K . E = \frac{1}{2} m v^{2} = \frac{P^{2}}{2 m}$

PHXI06:WORK ENERGY AND POWER

355424 A particle of mass $m$ at rest is acted upon by a force $P$ for a time $t$ . Its kinetic energy after an interval $t$ is

1

\frac{P^{2} t^{2}}{m}

2

\frac{P^{2} t^{2}}{2 m}

3

\frac{P^{2} t^{2}}{3 m}

4

\frac{P t}{2 m}

Explanation:

Given, force, $P = m a$
As the kinetic energy, $K = \frac{1}{2} m v^{2}$
$= \frac{1}{2} \frac{m^{2} (v^{2})}{m} = \frac{1}{2} \frac{m^{2} a^{2} t^{2}}{m}$
$(∵ v = a t, as u = 0)$
$= \frac{P^{2} t^{2}}{2 m} (∵ P = m a)$

PHXI06:WORK ENERGY AND POWER

355421 Four particles $A, B, C, D$ of mass $\frac{m}{2}, m, 2 m, 4 m$ , have same momentum, respectively. The particle with maximum kinetic energy is

1

C

2

A

3

D

4

B

Explanation:

$K E = \frac{p^{2}}{2 m}$
For same momentum $(p), K E \propto \frac{1}{m}$
Therefore, the lightest particle will possess maximum kinetic energy.
$∴$ A possess maximum kinetic energy.
So, correct option is (2).

JEE - 2024

PHXI06:WORK ENERGY AND POWER

355422 Two bodies are having kinetic energies in the ratio $16 : 9$ . If they have same linear momentum, the ratio of their masses respectively is

1

4 : 3

2

16 : 9

3

3 : 4

4

9 : 16

Explanation:

Kinetic energy of a body is given by
$K = \frac{p^{2}}{2 m}$
where, $p =$ momentum, $m =$ mass
$\Rightarrow \frac{K_{1}}{K_{2}} = {(\frac{p_{1}}{p_{2}})}^{2} (\frac{m_{2}}{m_{1}})$
Given, $p_{1} = p_{2}$
$\Rightarrow \frac{K_{1}}{K_{2}} = \frac{m_{2}}{m_{1}}$
$\Rightarrow \frac{m_{1}}{m_{2}} = \frac{K_{2}}{K_{1}} = \frac{9}{16}$

JEE - 2023

PHXI06:WORK ENERGY AND POWER

355423 Statement A :
A light body and a heavy body have same momentum. Then they also have same kinetic energy.
Statement B :
Kinetic energy does not depend on mass of the body

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

Explanation:

$K . E = \frac{1}{2} m v^{2} = \frac{P^{2}}{2 m}$

PHXI06:WORK ENERGY AND POWER

355424 A particle of mass $m$ at rest is acted upon by a force $P$ for a time $t$ . Its kinetic energy after an interval $t$ is

1

\frac{P^{2} t^{2}}{m}

2

\frac{P^{2} t^{2}}{2 m}

3

\frac{P^{2} t^{2}}{3 m}

4

\frac{P t}{2 m}

Explanation:

Given, force, $P = m a$
As the kinetic energy, $K = \frac{1}{2} m v^{2}$
$= \frac{1}{2} \frac{m^{2} (v^{2})}{m} = \frac{1}{2} \frac{m^{2} a^{2} t^{2}}{m}$
$(∵ v = a t, as u = 0)$
$= \frac{P^{2} t^{2}}{2 m} (∵ P = m a)$

PHXI06:WORK ENERGY AND POWER

355421 Four particles $A, B, C, D$ of mass $\frac{m}{2}, m, 2 m, 4 m$ , have same momentum, respectively. The particle with maximum kinetic energy is

1

C

2

A

3

D

4

B

Explanation:

$K E = \frac{p^{2}}{2 m}$
For same momentum $(p), K E \propto \frac{1}{m}$
Therefore, the lightest particle will possess maximum kinetic energy.
$∴$ A possess maximum kinetic energy.
So, correct option is (2).

JEE - 2024

PHXI06:WORK ENERGY AND POWER

355422 Two bodies are having kinetic energies in the ratio $16 : 9$ . If they have same linear momentum, the ratio of their masses respectively is

1

4 : 3

2

16 : 9

3

3 : 4

4

9 : 16

Explanation:

Kinetic energy of a body is given by
$K = \frac{p^{2}}{2 m}$
where, $p =$ momentum, $m =$ mass
$\Rightarrow \frac{K_{1}}{K_{2}} = {(\frac{p_{1}}{p_{2}})}^{2} (\frac{m_{2}}{m_{1}})$
Given, $p_{1} = p_{2}$
$\Rightarrow \frac{K_{1}}{K_{2}} = \frac{m_{2}}{m_{1}}$
$\Rightarrow \frac{m_{1}}{m_{2}} = \frac{K_{2}}{K_{1}} = \frac{9}{16}$

JEE - 2023

PHXI06:WORK ENERGY AND POWER

355423 Statement A :
A light body and a heavy body have same momentum. Then they also have same kinetic energy.
Statement B :
Kinetic energy does not depend on mass of the body

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

Explanation:

$K . E = \frac{1}{2} m v^{2} = \frac{P^{2}}{2 m}$

PHXI06:WORK ENERGY AND POWER

355424 A particle of mass $m$ at rest is acted upon by a force $P$ for a time $t$ . Its kinetic energy after an interval $t$ is

1

\frac{P^{2} t^{2}}{m}

2

\frac{P^{2} t^{2}}{2 m}

3

\frac{P^{2} t^{2}}{3 m}

4

\frac{P t}{2 m}

Explanation:

Given, force, $P = m a$
As the kinetic energy, $K = \frac{1}{2} m v^{2}$
$= \frac{1}{2} \frac{m^{2} (v^{2})}{m} = \frac{1}{2} \frac{m^{2} a^{2} t^{2}}{m}$
$(∵ v = a t, as u = 0)$
$= \frac{P^{2} t^{2}}{2 m} (∵ P = m a)$

PHXI06:WORK ENERGY AND POWER

355421 Four particles $A, B, C, D$ of mass $\frac{m}{2}, m, 2 m, 4 m$ , have same momentum, respectively. The particle with maximum kinetic energy is

1

C

2

A

3

D

4

B

Explanation:

$K E = \frac{p^{2}}{2 m}$
For same momentum $(p), K E \propto \frac{1}{m}$
Therefore, the lightest particle will possess maximum kinetic energy.
$∴$ A possess maximum kinetic energy.
So, correct option is (2).

JEE - 2024

PHXI06:WORK ENERGY AND POWER

355422 Two bodies are having kinetic energies in the ratio $16 : 9$ . If they have same linear momentum, the ratio of their masses respectively is

1

4 : 3

2

16 : 9

3

3 : 4

4

9 : 16

Explanation:

Kinetic energy of a body is given by
$K = \frac{p^{2}}{2 m}$
where, $p =$ momentum, $m =$ mass
$\Rightarrow \frac{K_{1}}{K_{2}} = {(\frac{p_{1}}{p_{2}})}^{2} (\frac{m_{2}}{m_{1}})$
Given, $p_{1} = p_{2}$
$\Rightarrow \frac{K_{1}}{K_{2}} = \frac{m_{2}}{m_{1}}$
$\Rightarrow \frac{m_{1}}{m_{2}} = \frac{K_{2}}{K_{1}} = \frac{9}{16}$

JEE - 2023

PHXI06:WORK ENERGY AND POWER

355423 Statement A :
A light body and a heavy body have same momentum. Then they also have same kinetic energy.
Statement B :
Kinetic energy does not depend on mass of the body

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both statements are correct.

4 Both Statements are incorrect.

Explanation:

$K . E = \frac{1}{2} m v^{2} = \frac{P^{2}}{2 m}$

PHXI06:WORK ENERGY AND POWER

355424 A particle of mass $m$ at rest is acted upon by a force $P$ for a time $t$ . Its kinetic energy after an interval $t$ is

1

\frac{P^{2} t^{2}}{m}

2

\frac{P^{2} t^{2}}{2 m}

3

\frac{P^{2} t^{2}}{3 m}

4

\frac{P t}{2 m}

Explanation:

Given, force, $P = m a$
As the kinetic energy, $K = \frac{1}{2} m v^{2}$
$= \frac{1}{2} \frac{m^{2} (v^{2})}{m} = \frac{1}{2} \frac{m^{2} a^{2} t^{2}}{m}$
$(∵ v = a t, as u = 0)$
$= \frac{P^{2} t^{2}}{2 m} (∵ P = m a)$

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