Q: Assertion: The relative velocity of the two particles in head-on elastic collision is unchanged both in magnitude and direction. Reason : The relative velocity is unchanged in magnitude but gets reversed in direction.

e=RVOARVOS For elastic collision e=1 ∴RVOS=RVOA Before collision they approach towards each other and after collision they recede from each other.

Q: If no external force acts on a system

(Correct option is A) Fext=dtdp Since Fext=0 ⇒dtdp=0 ∴p= constant

Question 1

Assertion: The relative velocity of the two particles in head-on elastic collision is unchanged both in magnitude and direction. Reason : The relative velocity is unchanged in magnitude but gets reversed in direction.

Accepted Answer

e=RVOARVOS​
For elastic collision e=1
∴RVOS=RVOA
Before collision they approach towards each other and after collision they recede from each other.

Question 2

Assertion: An object of mass m1​ and another of mass m2​(m2​>m1​) are released from certain distance. The objects move towards each other under the gravitational force between them. In this motion, centre of mass of their system will continuously move towards the heavier mass m2​ Reason : In a system of a heavier and a lighter mass, centre of mass lies closer to the heavier mass.

Accepted Answer

Centre of mass remains stationary.

Question 3

Assertion : A given force applied in turn to a number of different masses may cause the same rate of change in momentum in each but not the same acceleration to all. Reason : F=dtdp​ and a=mF​

Accepted Answer

The rate in change of momentum is independent of mass and by Newton's second law of motion it is equivalent to the applied external force.
While acceleration is force per unit mass, which is exactly same as the reason and hence (A) is true.

Question 4

Assertion : In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Reason : In an elastic collision, the linear momentum of the system is conserved.

Accepted Answer

Relative velocity of separation is equal to the relative velocity of approach. One of the case is shown below.Before collision, relative speed is 2 m/s and relative velocity of approach is 6 m/s.After collision, relative speed is 4 m/s and relative velocity of separation is 6 m/s.

Question 5

A ball is dropped from a height of 10 m. Ball is embedded in sand through 1 m and stops.

Accepted Answer

(Correct option is D)
For the Ball: weight of the ball and resistance due to sand are external forces. Hence, momentum is not conserved unless external force is zero.

Question 6

If no external force acts on a system

Accepted Answer

(Correct option is A)
Fext​=dtdp​
Since Fext​=0
⇒dtdp​=0
∴p= constant

Question 7

When two blocks connected by a spring move towards each other under mutual interaction

Accepted Answer

(Correct option is C)
The force interaction between the two blocks can be considered as internal forces if we take the two blocks plus spring as the system since there is no external force acting on this system.
The accelerations will be equal and opposite if masses are equal. Since the forces are internal, they will be equal and opposite.

Question 8

If two balls collide in air while moving vertically, then momentum of the system is conserved because

Accepted Answer

(Correct option is B)
The best option is (B), It is correct if force of gravity is much less compared to the impulsive force.
Option (A): Force of gravity will change the momentum of the system since it is an external force on the system.
Option (C): Impulsive force will be more than gravity, not less.
Option(D): Gravity will always act on the system, we cannot switch it off.

Question 9

When a cannon shell explodes in mid air, then identify the incorrect statement

Accepted Answer

(Correct option is B)
The momentum of the system in the horizontal direction is conserved since there is no external force in the horizontal direction.
The center of mass of the system before and after explosion will have the same trajectory.
We cannot say if the kinetic energy of the system always increases.

Question 10

In an inelastic collision

Accepted Answer

In inelastic collision momentum of the system is always conserved if Fext​=0. Velocity of separation is less than the velocity of approach since co-efficient of restitution e<1
e=0 for a perfectly inelastic collision since the colliding particles stick together after collision.
Hence, option (D) is correct.

Question 11

The momentum of a system is defined

Accepted Answer

(Correct option is D)vcm​=m1​+m2​+m3​+…..+mn​m1​v1​+m2​v2​+…..+mn​vn​​; ∴m1​+m2​+m3​+…..+mn​)vcm​=(m1​v1​+m2​v2​+…..+mn​vn​)Option(A) is LHS of the above equation.Option(B) is RHS of the above equation.Hence, (A) and(B) are same.Option (C) is correct since momentum can be defined for a body having translational motion, it may have additionally rotational and oscillatory motion.

Question 12

The momentum of a system with respect to centre of mass

Accepted Answer

(Correct option is C)
For a system, total momentum is always zero in the cm frame by definition since the momentum of the cm is zero in this frame.

Question 13

Three identical particles are located at the vertices of an equilateral triangle. Each particle moves along a meridian with equal speed towards the centroid and collides inelastically.

Accepted Answer

(Correct option is D)
Momentum of the three particle system will be conserved since there is no external force.
Option(A): We cannot say about its correctness from only momentum conservation.
Option(B): Though initial momentum and final momentum are zero, the particles can move after collision and make the final momentum zero also. Hence, it is incorrect.
Option(C): Since kinetic energy energy is not conserved in inelastic collision, it is possible that they will move with lesser speed but we cannot say that the particles will move in the original directions. Hence, it is incorrect.
Option(D): correct.

Question 14

The average resisting force that must act on a 5 kg mass to reduce its speed from 65 to 15 ms−1 in 2 s is

Accepted Answer

Impulse ∴Fav​​=Fav​(Δt)=∣ΔP∣=Δt∣ΔP∣​=Δtm(vi​−vf​)​=2(5)(65−15)​=125 N​

Question 15

In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance 1.2×10−10 m. The distance of the centre of mass from the carbon atom is

Accepted Answer

r2​r1​​r1​​=m1​m2​​=(m1​+m2​m2​​)d=(12+1616​)(1.2×10−10)=0.68×10−10 m​

Question 16

A bomb of mass 9 kg explodes into two pieces of masses 3 kg and 6 kg. The velocity of mass 3 kg is 16 ms−1. The kinetic energy of mass 6 kg is

Accepted Answer

3v1​v2​(KE)6 kg​​=6v2=63v1​​=63×16​=8 m/s=21​×6×(8)2=192 J​

Question 17

A heavy ball moving with speed v collides with a tiny ball. The collision is elastic, then immediately after the impact, the second ball will move with a speed approximately equal to

Accepted Answer

At rest
v2′​=(m1​+m2​m2​−m1​​)v1​+(m1​+m2​2m1​​)v2​
Substituting m2​≈0 and v1​=0 we get,
v2​≈2v

Question 18

A loaded 20,000 kg coal wagon is moving on a level track at 6 ms−1. Suddenly 5000 kg of coal is dropped out of the wagon. The final speed of the wagon is

Accepted Answer

Velocity of dropped out mass is also 6 m/s. So its relative velocity is zero and no thrust force will act. Therefore final speed remains 6 m/s.

Question 19

A machine gun shoots a 40 g bullet at a speed of 1200 ms−1. The man operating the gun can bear a maximum force of 144 N. The maximum number of bullets shot per second is

Accepted Answer

F=ΔtΔp​=n(mv)
Here n= number of bullets fired per second
⇒n=mvF​
=(40×10−3)(1200)144​=3

Question 20

A projectile of mass m is fired with a velocity v from point P at an angle 45∘. Neglecting air resistance, the magnitude of the change in momentum leaving the point P and arriving at Q is

Accepted Answer

∣Δp∣=∣ Impulse ∣=∣F⋅Δt∣
Here Δt=T=g2vsin45∘​=g2​v​
and ∣F∣=mg
∴∣Δp∣=(mg)(g2​v​)
=2​mv

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Solutions for Mechanics Volume 2 by DC Pandey

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