Centre of mass of a two-particle system and of a rigid body — practice questions

Question 1 · difficulty L2 · understanding

In a system two particles of masses $$m_1=3 \mathrm{~kg}$$ and $$m_2=2 \mathrm{~kg}$$ are placed at certain distance from each other. The particle of mass $$m_1$$ is moved towards the center of mass of the system through a distance $$2 \mathrm{~cm}$$. In order to keep the center of mass of the system at the original position, the particle of mass $$m_2$$ should move towards the center of mass by the distance _________ $$\mathrm{cm}$$.

Question 2 · difficulty L2 · understanding

Three identical spheres each of mass $2 \mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 \mathrm{~m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$, where the value of $x$ is ___________ .

Question 3 · difficulty L2 · understanding

A solid circular disc of mass $$50 \mathrm{~kg}$$ rolls along a horizontal floor so that its center of mass has a speed of $$0.4 \mathrm{~m} / \mathrm{s}$$. The absolute value of work done on the disc to stop it is ________ J.

Question 4 · difficulty L2 · understanding

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $$\sqrt x$$ m. The value of x is ____________.

Question 5 · difficulty L2 · understanding

The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by $$\left( {0,{{xR} \over \pi }} \right)$$. Then, the value of | x | is ______________.

Question 6 · difficulty L2 · understanding

Two identical bodies A and B of equal masses have initial velocities $\overrightarrow{v_1}=4 \hat{i} \mathrm{~m} / \mathrm{s}$ and $\overrightarrow{v_2}=4 \hat{j} \mathrm{~m} / \mathrm{s}$ respectively. The body A has acceleration $\overrightarrow{a_1}=6 \hat{i}+6 \hat{j} \mathrm{~m} / \mathrm{s}^2$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in $\_\_\_\_$ path.

• A. circular
• B. parabolic
• C. straight line
• D. elliptical

Question 7 · difficulty L2 · understanding

A rod of length 5 L is bent right angle keeping one side length as 2 L . The position of the centre of mass of the system : (Consider $\mathrm{L}=10 \mathrm{~cm}$)

• A. $4 \hat{i}+9 \hat{j}$
• B. $2 \hat{i}+3 \hat{j}$
• C. $5 \hat{i}+8 \hat{j}$
• D. $3 \hat{i}+7 \hat{j}$

Question 8 · difficulty L2 · understanding

Two bodies of mass $$1 \mathrm{~kg}$$ and $$3 \mathrm{~kg}$$ have position vectors $$\hat{i}+2 \hat{j}+\hat{k}$$ and $$-3 \hat{i}-2 \hat{j}+\hat{k}$$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

• A. $$\hat{i}+2 \hat{j}+\hat{k}$$
• B. $$-3 \hat{i}-2 \hat{j}+\hat{k}$$
• C. $$-2 \hat{i}+2 \hat{k}$$
• D. $$2 \hat{i}-\hat{j}+2 \hat{k}$$

Question 9 · difficulty L2 · understanding

Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre of mass of the system unchanged is :

• A. 4 cm towards the 10 kg block
• B. 2 cm away from the 10 kg block
• C. 2 cm towards the 10 kg block
• D. 4 cm away from the 10 kg block

Question 10 · difficulty L3 · understanding

A uniform thin metal plate of mass $$10 \mathrm{~kg}$$ with dimensions is shown. The ratio of $$\mathrm{x}$$ and y coordinates of center of mass of plate in $$\frac{n}{9}$$. The value of $$n$$ is ________.