Collisions(12th Grade > Physics ) Questions and answers for exam Preparation

12th Grade > Physics

COLLISIONS MCQs

Total Questions : 29 | Page 1 of 3 pages

Question 1. A ball P of mass 2 kg undergoes an elastic collision with another ball Q initially kept at rest. After the collision, ball P continues to move in its original direction with a speed one-fourth of its original speed. What is the mass of ball Q?

0.9 kg
1.2 kg
1.5 kg
1.8 kg

Discuss Question

Answer: Option B. -> 1.2 kg
:
B
Since the collision is elastic, both momentum and kinetic energy are conserved. If m is mass of ball Qand v’ its speed after the collision, the law of conservation of momentum gives

2 v = 2 \times \frac{v}{4} + m v^{^{'}}

Where v is the original speed of ball P. thus

m v^{^{'}} = \frac{3 v}{2} o r v^{^{'}} = \frac{3 v}{2 m}

(i)
The law of conservation of energy gives

\frac{1}{2} \times 2 \times v^{2} = \frac{1}{2} \times 2 \times {(\frac{v}{4})}^{2} + \frac{1}{2} m v^{^{'} 2}

m v^{^{'} 2} = \frac{15 v^{2}}{8}

(ii)
Using (i) in (ii) we get m = 1.2 kg. Hence the correct choice is (b).

Question 2. When two bodies stick together after collision, the collision is said to be

Partially elastic
Total elastic
Total inelastic
None of the above

Discuss Question

Answer: Option C. -> Total inelastic
:
C
By definition of Perfectly Inelastic Collision, the two colliding bodies stick together after collision

Question 3. A body of mass 5 kg is moving along the x-axis with a velocity 2

m s^{- 1}

. Another body of mass 10 kg is moving along the y-axis with a velocity

\sqrt{3} m s^{- 1}

. If they collide at the origin and stick together, then the final velocity of the combined mass is

√3ms−1
(√3+1)ms−1
43ms−1
None

Discuss Question

Answer: Option C. -> 43ms−1
:
C
Momentum of 5 kg mass

(p_{1}) = 5 \times 2 = 10 k g m s^{- 1}

along the x-axis. Momentum of 10 kg mass

(p_{2}) = 10 \sqrt{3} k g m s^{- 1}

along the y-axis. These two momenta are perpendicular to each other.
Therefore, the resultant initial momentum is

P = \sqrt{p_{1}^{2} + p_{2}^{2}} = \sqrt{(10)^{2} + (10 \sqrt{3})^{2}} = 20 k g m s^{- 1}

If v

m s^{- 1}

is the velocity of the combined mass, then the final momentum = (10 + 5) v = 15 v kg

m s^{- 1}

Now, from the principle of conservation of momentum, we have 15 v = 20 or

v = \frac{4}{3} m s^{- 1}

, which is choice (c).

Question 4. A body of mass 'm' moving with a speed 'v' suffers an inelastic collision with another body of 'M' at rest and sticks to it, the ratio of the final kinetic energy of the system to the initial kinetic energy is

(mm+M)
(Mm+M)
(m+Mm)
(m+MM)

Discuss Question

Answer: Option A. -> (mm+M)
:
A
Apply conservation of momentum to find the speed of system after collision
Initial

K E = \frac{1}{2} m v^{2} . F i n a l K E = \frac{1}{2} (m + M) V^{2}

. Therefore,

\frac{F i n a l K E}{I n i t i a l K E} = (\frac{m + M}{m}) \frac{V^{2}}{v^{2}} = \frac{m}{m + M}

Hence the correct choice is (a).

Question 5. A radioactive nucleus of mass number 'A', initially at rest, emits an

α

- particle with a speed 'v'. What will be the recoil speed of the daughter nucleus?

2vA−4
2vA+4
4vA−4
4vA+4

Discuss Question

Answer: Option C. -> 4vA−4
:
C
The total number of nucleons (i.e. protons + neutrons) in a nucleus is called its mass number. An α-particleis a helium nucleus having 2 protons and 2 neutrons. So the mass number of an

α

- particle = 4. When anucleus of mass number A emits an

α

- particle, the mass number of the daughter nucleus reduces to(A – 4). If V is the recoil speed of the daughter nucleus, we have, from the law of conservation ofmomentum, (A – 4)V-4v = 0
or

V = \frac{4 v}{A - 4}

Hence the correct choice is (c)

Question 6. The coefficient of restitution 'e' for a perfectly elastic collision is

1
0
∞
-1

Discuss Question

Answer: Option A. -> 1
:
A
No energy is lost in perfectly elastic collision. Therefore e = 1

Question 7. A sphere of mass 'm' moving with a constant velocity 'u' hits another stationary sphere of the same mass. If 'e' is the coefficient of restitution, then the ratio of the velocity of two spheres after collision will be

1−e1+e
1+e1−e
e+1e−1
e+1e−1t2

Discuss Question

Answer: Option A. -> 1−e1+e
:
A
Let the final velocities of the two masses be

v_{1}

and

v_{2}

By definition,

e = \frac{v_{2} - v_{1}}{0 - 4}

Conservation of linear momentum,

m (u) + 0 = m v_{1} + m v_{2}

\Rightarrow v_{1} + v_{2} = 4

∴ \frac{v_{1} + v_{2}}{v_{2} - v_{1}} = \frac{4}{- e 4}

\frac{v_{1} + v_{2}}{v_{1} - v_{2}} = \frac{1}{e}

∴ \frac{v_{1}}{v_{2}} = \frac{1 + e}{1 - e}

\frac{v_{2}}{v_{1}} = \frac{1 - e}{1 + e}

Question 8. A body of mass 2 kg moving with a velocity of 3 m/sec collides head on with a body of mass 1 kg moving in opposite direction with a velocity of 4 m/sec. After collision, two bodies stick together and move with a common velocity which in m/sec is equal to

Discuss Question

Answer: Option C. -> 23
:
C

m_{1} v_{1} - m_{2} v_{2} = (m_{1} + m_{2}) v

\Rightarrow (2 \times 3) - (1 \times 4) = (2 + 1) v \Rightarrow v = \frac{2}{3} m / s

Question 9. A shell initially at rest explodes into two pieces of equal mass, then the two pieces will

Be at rest
Move with different velocities in different directions
Move with the same velocity in opposite directions
Move with the same velocity in same direction

Discuss Question

Answer: Option C. -> Move with the same velocity in opposite directions
:
C
According to law of conservation of linear momentum both pieces should possess equal momentum after explosion. As their masses are equal therefore they will possess equal speed in opposite direction.

Question 10. A body of mass 'm' moving with a velocity 'v' in the x-direction collides with a body of mass 'M' moving with a velocity 'V' in the y-direction. They stick together during a collision. Then

The magnitude of the momentum of the composite body is √(mv)2+(MV)2
The composite body moves in a direction making a angle θ=tan−1(MVmv) with the x-axis.
The loss of kinetic energy as a result of collision is 12Mm(M+m)(V2+v2)
All the above choices are correct.

Discuss Question

Answer: Option D. -> All the above choices are correct.
:
D
Refer to Figure Here p = mv and P = MV.