Center of Mass and Mass Moments – Rankers Physics

Calculation of Center of Mass: Practice Problem & Solution

Assertion (A): The centre of mass of a system of two particles is closer to the heavier particle. Reason (R): Algebraic sum of mass moments about centre of mass is zero.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Calculation of Center of Mass. Understanding the underlying formula is key to arriving at the correct answer below:

For a two-particle system, the center of mass \( R_{CM} \) is defined such that the sum of mass moments about it is zero: \( m_1r_1 = m_2r_2 \). If \( m_1 > m_2 \), then \( r_1 < r_2 \), meaning the COM is closer to the heavier particle.

Thus both A and R are true, and R explains A.

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Assertion (A): In case of bullet fired from a gun, the ratio of kinetic energy of gun and bullet is equal to ratio of masses of bullet and gun. Reason (R): In firing of bullet, linear momentum of system is conserved.  
2. A mass of \( 1 \text{ kg} \) is thrown up with a velocity of \( 100 \text{ m/s} \). After \( 5 \) seconds, it explodes into two parts. One part of mass \( 400 \text{ g} \) comes down with a velocity \( 25 \text{ m/s} \). Calculate the velocity of other part: (2000)
3. A moving block having mass $m$, collides with another stationary block having mass $4m$. The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v$, then the value of coefficient of restitution ($e$) will be (2018)
4. A body with kinetic energy K moving in +X direction splits up into two parts A and B of equal mass on its own. Part 'A' moves back in -X direction with a velocity equal in magnitude to the initial velocity of the body. The kinetic energy of part B will be:
5. Assertion (A): In a perfectly inelastic collision there is a limit to the loss of kinetic energy of colliding bodies. Reason (R): In perfectly inelastic collision, linear momentum of system is conserved.