Two particles of mass $5\,kg$ and $10\,kg$ respectively are attached to the two ends of a rigid rod of length 1m with negligible mass.
The centre of mass of the system from the $5\,kg$ particle is nearly at a distance of :
- 33 cm
- 50 cm
- 67 cm
- 80 cm
The Correct Option is C
Solution and Explanation
$x_{cm}=\frac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}$
$=\frac{5 \times 0+100 \times 10}{5+10}$
$=\frac{200}{2}$
$=66.66\,cm$
$x_{cm}=67\,cm$
Top Questions on Centre of mass
- Three blocks A, B and C are arranged as shown in the figure such that the distance between two successive blocks is 10 m. Block A is displaced towards block B by 2 m and block C is displaced towards block B by 3 m. The distance through which the block B should be moved so that the centre of mass of the system does not change is
- AP EAPCET - 2025
- Physics
- Centre of mass
- The angular velocity of a body changes from \(6 \, \text{rad/s}\) to \(21 \, \text{rad/s}\) in a time of \(1.5 \, \text{s}\). If the moment of inertia of the body is \(100 \, \text{g m}^2\), then the rate of change of angular momentum of the body is
- AP EAPCET - 2025
- Physics
- Centre of mass
- A circular disc of diameter 0.8 m and mass 4 kg is rolling on a smooth horizontal plane. If 2.56 N torque is acting on the disc, then its angular acceleration is:
- AP EAPCET - 2025
- Physics
- Centre of mass
- Radius of gyration of a thin uniform rod of length \( L \) about an axis passing through its centre and perpendicular to its length is:
- AP EAPCET - 2025
- Physics
- Centre of mass
- Radius of gyration of a thin uniform rod of length \( L \) about an axis passing through its centre and perpendicular to its length is:
- AP EAPCET - 2025
- Physics
- Centre of mass
Questions Asked in NEET exam
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A typical unfertilized, angiosperm embryo sac at maturity is 8-nucleate and 7-celled.
Reason (R): The egg apparatus has 2 polar nuclei.In the light of the above statements, choose the correct answer from the options given below:
- NEET (UG) - 2025
- Angiosperms
- A ball of mass 0.5 kg is dropped from a height of 10 m. The ball hits the ground and rises to a height of 1.5 m. The impulse imparted to the ball during its collision with the ground is : (Take \(g = 9.8 \, \text{m/s}^2\))
- NEET (UG) - 2025
- Collision and Impulse
- Consider the diameter of a spherical object being measured with the help of a Vernier Callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least count in the M.S. is 0.1 cm and the zero of V.S. is at -0.1 cm when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is \(M = 5\) cm and the number of coinciding vernier division is 8, the measured diameter after zero error correction, is:
- NEET (UG) - 2025
- Measurement of length
- A container has two chambers of volumes \(V_1 = 2\) litres and \(V_2 = 3\) litres separated by a partition made of a thermal insulator. The chambers contain \(n_1 = 2\) moles and \(n_2 = 3\) moles of ideal gas at pressures \(p_1 = 1\) atm and \(p_2 = 2\) atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of :
- NEET (UG) - 2025
- Ideal Gases
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :
- NEET (UG) - 2025
- Moment Of Inertia
Concepts Used:
Center of Mass
The center of mass of a body or system of a particle is defined as a point where the whole of the mass of the body or all the masses of a set of particles appeared to be concentrated.
The formula for the Centre of Mass:
Center of Gravity
The imaginary point through which on an object or a system, the force of Gravity is acted upon is known as the Centre of Gravity of that system. Usually, it is assumed while doing mechanical problems that the gravitational field is uniform which means that the Centre of Gravity and the Centre of Mass is at the same position.