Conservation of Momentum and Mechanical Energy

Q 1 :
A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is [2024]

6
2
3
5

1

2

3

4

(4)

Momentum will remain conserve

$1000 \times 6 = 1200 \times v$

$v = 5 m / s$

Q 2 :
A stationary particle breaks into two parts of masses $m_{A}$ and $m_{B}$ , which move with velocities $v_{A}$ and $v_{B}$ respectively. The ratio of their kinetic energies $(K_{B} : K_{A})$ is [2024]

$m_{B} : m_{A}$
$1 : 1$
$m_{B} v_{B} : m_{A} v_{A}$
$v_{B} : v_{A}$

1

2

3

4

(4)

By conservation of linear momentum

$0 = m_{A} \vec{V_{A}} + m_{B} \vec{V_{B}}$

$\Rightarrow m_{A} \vec{V_{A}} = - m_{B} \vec{V_{B}}$

$\Rightarrow m_{A} V_{A} = m_{B} V_{B}$

$K = \frac{P^{2}}{2 m} \Rightarrow K \propto \frac{1}{m}$

$\Rightarrow \frac{K_{B}}{K_{A}} = \frac{m_{A}}{m_{B}} \Rightarrow \frac{K_{B}}{K_{A}} = \frac{v_{B}}{v_{A}}$

Q 3 :
A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration, they will move [2024]

in opposite directions with speed in the ratio of 1:2 respectively
in opposite directions with speed in the ratio of 2:1 respectively
in the same direction with the same speed.
in opposite directions with the same speed.

1

2

3

4

(1)

From conservation of momentum

$P_{i} = P_{f}$

$0 = m v_{1} - 2 m v_{2}$

$\frac{v_{1}}{v_{2}} = \frac{2}{1},$ move in opposite direction with speed ratio 1 : 2.

Q 4 :
Consider two blocks A and B of masses $m_{1}$ = 10 kg and $m_{2}$ = 5 kg that are placed on a frictionless table. The block A moves with a constant speed v = 3 m/s towards the block B kept at rest. A spring with spring constant k = 3000 N/m is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring) [2025]

0.2 m
0.4 m
0.1 m
0.3 m

1

2

3

4

(3)

Conservation of Linear momentum,

$m_{1} v_{1} + m_{2} v_{2} = (m_{1} + m_{2}) v_{cm}$

$v_{cm} \Rightarrow \frac{10 \times 3}{10 + 5} \Rightarrow \frac{30}{15} = 2 m / s$

Conservation of mechanical energy,

$\frac{1}{2} k x^{2} = \frac{1}{2} (10) {(3)}^{2} - [\frac{1}{2} (15) {(2)}^{2}]$

$\Rightarrow 3000 x^{2} = 90 - 60 = 30$

$\Rightarrow x^{2} = \frac{30}{3000} = \frac{1}{100}$

$\Rightarrow x = \frac{1}{10} m$

Topic Question Set

Q 1 :
A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is [2024]

Q 2 :
A stationary particle breaks into two parts of masses $m_{A}$ and $m_{B}$ , which move with velocities $v_{A}$ and $v_{B}$ respectively. The ratio of their kinetic energies $(K_{B} : K_{A})$ is [2024]

Q 3 :
A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration, they will move [2024]

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Topic Question Set

Q 1 : A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is [2024]

Q 2 : A stationary particle breaks into two parts of masses mA and mB, which move with velocities vA and vB respectively. The ratio of their kinetic energies (KB:KA) is [2024]

Q 3 : A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration, they will move [2024]

Want Us to Email you About Special Offers & Updates?

Q 1 :
A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is [2024]

Q 2 :
A stationary particle breaks into two parts of masses $m_{A}$ and $m_{B}$ , which move with velocities $v_{A}$ and $v_{B}$ respectively. The ratio of their kinetic energies $(K_{B} : K_{A})$ is [2024]

Q 3 :
A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration, they will move [2024]