Case Study Questions for Class 11 Physics Chapter 7 System of Particles and Rotational Motion

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Here we are providing case study questions for class 11 physics chapter 7 System of Particles and Rotational Motion. Students can practice these questions for better understanding of case study type questions.

Case Study Questions for Class 11 Physics Chapter 7 System of Particles and Rotational Motion

1 Case Studies · 4 Questions · With Answer & Explanation

Case Study: Centre of Mass

Read the passage carefully, then answer all four questions

Ch 7 · System of Particles and Rotational Motion

The centre of mass of a body or a system of bodies is the point which moves as though all of the mass were concentrated there and all external forces were applied to it. Hence, a point at which the entire mass of the body or system of bodies is supposed to be concentrated is known as the centre of mass.

If a system consists of more than one particle (or bodies) and net external force on the system in a particular direction is zero with centre of mass at rest. Then, the centre of mass will not move along that direction. Even though some particles of the system may move along that direction.

Two bodies of masses 1 kg and 2 kg are lying in xy-plane at (-1, 2) and (2, 4), respectively. What are the coordinates of the centre of mass?

a 1, 10/3

b (1, 0)

c (0, 1)

d None of these

Correct Answer (a) 1, 10/3 ✅

Explanation

The coordinates of the centre of mass $(X_{cm}, Y_{cm})$ are calculated using the formulas:

$$X_{cm} = \frac{m_1x_1 + m_2x_2}{m_1 + m_2}$$

$$Y_{cm} = \frac{m_1y_1 + m_2y_2}{m_1 + m_2}$$

Plugging in the given values ($m_1 = 1$, $x_1 = -1$, $y_1 = 2$ and $m_2 = 2$, $x_2 = 2$, $y_2 = 4$):

$$X_{cm} = \frac{1(-1) + 2(2)}{1 + 2} = \frac{3}{3} = 1$$

$$Y_{cm} = \frac{1(2) + 2(4)}{1 + 2} = \frac{10}{3}$$

Two balls of same masses start moving towards each other due to gravitational attraction, if the initial distance between them is L. Then, they meet at:

a L/2

b L

c L/3

d L/4

Correct Answer (a) L/2 ✅

Explanation

Since the two balls have the same mass, their centre of mass lies exactly at the midpoint between them. The gravitational attraction is an internal force, meaning the net external force is zero. Therefore, the centre of mass remains at rest, and the two balls will meet exactly at the centre of mass, which is at a distance of L/2.

iii

The centre of mass of a system of two particles divides the distance between them:

a in inverse ratio of square of masses of particles

b in direct ratio of square of masses of particles

c in inverse ratio of masses of particles

d in direct ratio of masses of particles

Correct Answer (c) in inverse ratio of masses of particles ✅

Explanation

For a two-particle system with the centre of mass at the origin, $m_1r_1 = m_2r_2$, where $r_1$ and $r_2$ are the distances of the masses from the centre of mass. This can be rewritten as $\frac{r_1}{r_2} = \frac{m_2}{m_1}$. This demonstrates that the centre of mass divides the internal distance in the inverse ratio of their masses.

Two particles A and B initially at rest move towards each other under a mutual force of attraction. At the instant, when the speed of A is v and the speed of B is 2v, the speed of centre of mass of the system is:

a zero

b v

c 1.5 v

d 3v

Correct Answer (a) zero ✅

Explanation

The particles are moving towards each other solely due to their mutual force of attraction, which acts as an internal force. Since they are initially at rest, the initial velocity of the centre of mass is zero. Because there is no net external force acting on the system ($F_{ext} = 0$), the acceleration of the centre of mass is zero, and its velocity remains constant at zero regardless of the individual speeds of particles A and B.

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Case Study Questions for Class 11 Physics Chapter 7 System of Particles and Rotational Motion

Case Study Questions for Class 11 Physics Chapter 7 System of Particles and Rotational Motion

Case Study: Centre of Mass

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Case Study Questions for Class 11 Physics Chapter 7 System of Particles and Rotational Motion

Case Study: Centre of Mass

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