A rigid body consists of a 3 kg mass connected to a 2 kg mass by a massless rod. The 3 kg mass is located at r → = ( 2 i ^ + 5 j ^ ) m and the 2 kg mass at r → 2 = ( 4 i ^ + 2 j ^ ) m . Find the position and coordinates of the centre of mass.

We know that distance between the two point is equal to the magnitude of the position vector of the line joining the two point. Given r 1 = 2 i + 5 j r 2 = 4 i + 2 j Hence, r 1 r 2 = ( 4 - 2 ) i + ( 2 - 5 ) j = 2 i - 3 j . Hence | r 1 r 2 | = ( 2 ² + 3 ² ) = 13 Hence, length of the rod is 13 m . Centre of mass, r = ( m 1 r 1 + m 2 r 2 ) m 1 + m 2 = 3 ( 2 i + 5 j ) + 2 ( 4 i + 2 j ) 5 = ( 14 i + 19 j ) 5 = 14 5 i + 19 5 j Hence, the centre of mass is at 14 5 i ^ + 19 5 j ^ m , ( 2 . 8 , 3 . 8 ) .

EASY

NEET

IMPORTANT

Earn 100

A force of $10 N$ acts on a body for $3 μ s$ . If the mass of the body is $5 g$ , calculate the impulse and the change in velocity.

Important Questions on Centre of Mass, Momentum and Collisions

EASY

NEET

IMPORTANT

Beta Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>BEGINNER'S BOX - 1>Q 3

A batsman deflects a ball by an angle of

45 °

without changing its initial speed, which is equal to

54 km / h

. What is the impulse imparted to the ball? (Mass of the ball is

0.15 kg

)

MEDIUM

NEET

IMPORTANT

Beta Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>BEGINNER'S BOX - 1>Q 4

The magnitude of the force (in newton) acting on a body varies with time $t$ (in microsecond) as shown in the figure $A B$ , $B C$ and $C D$ are straight line segments. Find the magnitude of the total impulse of the force (in $N - s$ ) on the body from $t = 4 μs$ to $t = 16 μs$ .

Question Image

MEDIUM

NEET

IMPORTANT

Beta Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>BEGINNER'S BOX - 1>Q 5

What are the coordinates of the centre of mass of the three particles system shown in the figure?
Question Image

MEDIUM

NEET

IMPORTANT

Beta Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>BEGINNER'S BOX - 1>Q 6

Four particles of masses $m, 2 m, 3 m, 4 m$ are placed at the corners of a square of side $a$ as shown in figure. Find out the coordinates of the centre of mass.

Question Image

MEDIUM

NEET

IMPORTANT

Beta Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>BEGINNER'S BOX - 1>Q 7

A rigid body consists of a

3 kg

mass connected to a

2 kg

mass by a massless rod. The

3 kg

mass is located at

\vec{r} = (2 \hat{i} + 5 \hat{j}) m

and the

2 kg

mass at

{\vec{r}}_{2} = (4 \hat{i} + 2 \hat{j}) m

. Find the position and coordinates of the centre of mass.

MEDIUM

NEET

IMPORTANT

Beta Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>BEGINNER'S BOX - 1>Q 8

Figure shows a uniform square plate from which one or more of the four identical squares at the corners will be removed.
Question Image

(a) Where is the centre of mass of the plate originally?
(b) Where is the C.M. after square

1

is removed?
(c) Where is the C.M. after squares

1

and

2

removed?
(d) Where is the C.M. after squares

1

and

3

are removed?
(e) Where is the C.M. after squares

1, 2

and

3

are removed?
(f) Where is the C.M. after all the four squares are removed?
Give your answers in terms of quadrants and axis.

MEDIUM

NEET

IMPORTANT

Beta Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>BEGINNER'S BOX - 1>Q 9

Find the centre of mass of a uniform disc of radius

a

from which a circular section of radius

b

has been removed. The centre of the hole is at a distance

c

from the centre of the disc.

EASY

NEET

IMPORTANT

Beta Question Bank for Medical: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>BEGINNER'S BOX - 2>Q 2

Find the velocity of centre of mass of the system as shown in the figure is

Question Image

A force of 10 N acts on a body for 3 μ s. If the mass of the body is 5 g, calculate the impulse and the change in velocity.

Important Questions on Centre of Mass, Momentum and Collisions

Learn and Prepare for any exam you want !

A force of $10 N$ acts on a body for $3 μ s$ . If the mass of the body is $5 g$ , calculate the impulse and the change in velocity.