Centre Of Mass MCQ Level - 1

# Centre Of Mass MCQ Level - 1

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Centre Of Mass MCQ Level - 1 for IIT JAM 2022 is part of Topic wise Tests for IIT JAM Physics preparation. The Centre Of Mass MCQ Level - 1 questions and answers have been prepared according to the IIT JAM exam syllabus.The Centre Of Mass MCQ Level - 1 MCQs are made for IIT JAM 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Centre Of Mass MCQ Level - 1 below.
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Centre Of Mass MCQ Level - 1 - Question 1

### A particle of mass m moving with velocity u1 collides elastically with another particle of same mass moving with velocity u2 in the same direction. After collision their speeds are v1 and v2 respectively then (A) u1 + v1 = v2 + u2 (B) u1 – v1 = v2 + u2

Detailed Solution for Centre Of Mass MCQ Level - 1 - Question 1

Equation A is correct but not B

(For elastic collision e = 1)
⇒ 1(u2 – u1) = –(v2 – v1)
⇒ u2 + v2 = u1 + v1
The correct answer is: Equation A is correct but not B

Centre Of Mass MCQ Level - 1 - Question 2

### The centre of the mass of the shaded portion of the disc is : (The mass is uniformly distributed in the shaded portion) :

Detailed Solution for Centre Of Mass MCQ Level - 1 - Question 2

The correct answer is: R/20 to the left of A

Centre Of Mass MCQ Level - 1 - Question 3

### A man of mass M hanging with a light rope which is connected with a balloon of mass m. The system is at rest in air. When man rises a distance h with respect to balloon. Find the distance raised by man :

Detailed Solution for Centre Of Mass MCQ Level - 1 - Question 3

Initially

since no external force is acting

∴ COM should be at rest

Let balloon descend by a distance x.

Mh = (m + M)x

(Distance descend by balloon)

(Distance raised by man)

Centre Of Mass MCQ Level - 1 - Question 4

The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is :

Detailed Solution for Centre Of Mass MCQ Level - 1 - Question 4

According to conservation of energy

MkL2 = p2     (p = mu)

Centre Of Mass MCQ Level - 1 - Question 5

A particle of mass 4m which is at rest explodes into three fragments. Two of the fragments each of mass  m  are found to move with a speed v each in mutually perpendicular directions. The minimum energy released in the process of explosion is :

Detailed Solution for Centre Of Mass MCQ Level - 1 - Question 5

The correct answer is: (3/2) mv2

Centre Of Mass MCQ Level - 1 - Question 6

Find the position of centre of mass of the uniform planar sheet shown in figure with respect to the origin (O) :

Detailed Solution for Centre Of Mass MCQ Level - 1 - Question 6

Centre Of Mass MCQ Level - 1 - Question 7

A ball of mass m strikes the fixed inclined plane after falling through a height h. If it rebounds elastically, the impulse on the ball is :

Detailed Solution for Centre Of Mass MCQ Level - 1 - Question 7

Here e = 1
If ball rebounded elastically
vLOI = uLOI

∴ Along line of impact momentum conservation

Along line of impact

Centre Of Mass MCQ Level - 1 - Question 8

The spacecraft of mass M moves with velocity V in free space at first, then it explodes breaking into two pieces. If after explosion a piece of mass m comes to rest, the other piece of space craft will have :

Detailed Solution for Centre Of Mass MCQ Level - 1 - Question 8

Initial momentum of the system  Pi = MV
Let the mass of one part be m
Its velocity  V = 0
So, mass of other part  m′ = M − m
Let its velocity be V′.
Final momentum of the system Pf = mV + m′V′
Or Pf = 0+(M−m)V' = (M−m)V′
Applying the conservation of linear momentum   Pf = Pi
∴ (M−m)V' = MV
⟹ V'= MV/(M-m)

Centre Of Mass MCQ Level - 1 - Question 9

A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half the kinetic energy is lost by impact. What is the value of the coefficient of restitution?

Detailed Solution for Centre Of Mass MCQ Level - 1 - Question 9

Centre Of Mass MCQ Level - 1 - Question 10

A bullet of mass a  and velocity b is fired into a large block of mass c. The final velocity of the system is :

Detailed Solution for Centre Of Mass MCQ Level - 1 - Question 10

From momentum conservation Pi = Pf
ab = (a + c)v

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