NEET Physics: Centre of the mass of a rigid body Practice Questions

Q1. The concept of the center of mass is essential in analyzing rotational motion because it relates the linear motion of the body to its rotational properties. Which property is directly related to the distribution of mass about the center of mass?

• ALinear momentum.
• BAngular momentum.
• CMoment of inertia.
• DTorque.

Q2. What is the centre of mass (CM) of a particle, according to the definition in rotational mechanics?

• AThe point where the position vector of the CM is defined.
• BThe point where the net torque is zero.
• CThe point where the net gravitational force is zero.
• DThe average position of all mass elements of the body.

Q3. A solid sphere of uniform density is rotating about an axis passing through its centre of mass. What is the position of the centre of mass relative to the axis of rotation?

• AAt the surface of the sphere
• BAt the centre of the sphere
• CAt a distance equal to the radius
• DIt depends on the rotation speed

Q4. A uniform thin rod of length L is rotating about an axis passing through its center. What is the location of the center of mass of the rod?

• ADepends on the axis of rotation
• BAt the geometric center
• CAt an arbitrary point
• DAt one end

Q5. If a body is distributed uniformly along a straight line, the centre of mass of the body is located at:

• AThe geometric centre.
• BThe midpoint of the body.
• CAny point on the line.
• DThe end of the body with the greater mass.

Q6. For a hollow cylinder of uniform density, the center of mass is located at which point?

• AAt the surface of the cylinder
• BAt the centroid of the entire volume
• CAt the axis of symmetry
• DAt the geometric center of the cross-section

Q7. The centre of mass of a uniform rod of length L is located at which point?

• AAt one end
• BAt the center of the circle defined by its ends
• CAt the midpoint
• DAt the point where the moment of inertia is minimum

Q8. The center of mass of a system of particles is the unique point where the weighted average of the positions of the particles is taken. Which of the following statements is true regarding the center of mass?

• AIt is always located at the geometric center of the body.
• BIt is the point where the moment of inertia is zero.
• CIt is a point mass that represents the entire mass of the body.
• DIt is the point where the net external force acts.

Q9. If the entire mass distribution of a rigid body is perfectly symmetric about a line, the center of mass must lie on that line. This statement is based on which fundamental property of the center of mass?

• ASymmetry of mass distribution
• BAngular Momentum conservation
• CForce application
• DMoment of Inertia

Q10. A system consists of two masses, m_A = 5 kg and m_B = 15 kg, separated by a distance of 2 m. If m_A is at x=0 m and m_B is at x=2 m, what is the position of the center of mass of the system?

• A3 m
• B1 m
• C1.5 m
• D2 m

Q11. If the centre of mass of a rigid body is fixed, how does the distribution of mass affect the body's rotational properties?

• AIt determines the torque required for rotation
• BIt determines the axis of rotation.
• CIt affects only the linear momentum.
• DIt does not affect the moment of inertia.

Q12. For a thin ring rotating about its diameter, where is the centre of mass of the ring located?

• AAt the edge farthest from the axis
• BAt the circumference
• CThe centre of the circle defined by its ends
• DAt the centre of the ring

Q13. When calculating the center of mass of a thin wire rotating about an axis, the mass distribution along the wire determines the location of the center of mass. If the wire has uniform mass density, how is the center of mass located?

• AAt one end of the wire.
• BAt the geometric center of the wire.
• CAt the midpoint of the wire.
• DIt depends on the axis of rotation.

Q14. For a system of two point masses m₁ at position x₁ and m₂ at position x₂, the position of the center of mass (X₍cm)) is given by the formula:

• AX₍cm) = (m₁ + m₂) / 2
• BX₍cm) = m₁ x₁ / m₂
• CX₍cm) = m₁ x₁ + m₂ x₂
• DX₍cm) = (m₁ x₁ + m₂ x₂) / (m₁ - m₂)

Q15. If a body rotates about a fixed axis, the motion of its center of mass is governed by which principle?

• ACentripetal Acceleration
• BNewton's First Law (Inertia)
• CGravitational Force
• DConservation of Angular Momentum