Question

# Two particles of mass 5 kg and 10 kg
respectively are attached to the two ends of a
rigid rod of length 1 m with negligible mass.
The centre of mass of the system from the 5 kg
particle is nearly at a distance of:
(1) 50 cm
(2) 67 cm
(3) 80 cm
(4) 33 cm​

Answer 1

Given :

Two particles of mass 5kg and 10kg respectively are attached to the two ends of a rigid rod of length 1m with negligible mass.

To Find :

The centre of mass of the system from the 5kg particle.

Solution :

❖ Centre of mass is an Imaginary point where the whole mass of system can be assumed to be concentrated.

The position of the centre of mass of a two particle system is

$\dag\:\underline{\boxed{\bf{\orange{x_{CM}=\dfrac{m_1x_1+m_2x_2}{m_1+m_2)}}}}}$

By substituting the given values;

$\sf:\implies\:x_{CM}=\dfrac{(5)(0)+(10)(1)}{5+10}$

$\sf:\implies\:x_{CM}=\dfrac{0+10}{15}$

$\sf:\implies\:x_{CM}=\dfrac{10}{15}$

$:\implies\:\underline{\boxed{\bf{\purple{x_{CM}=0.67\:m=67\:cm}}}}$

∴ (2} is the correct answer!

Knowledge BoosteR :

• In rigid body, the distances between all pairs of particles do not change.
• The centre of mass of an object need not lie within the object.
• When the total external force on the system is zero, the velocity of the centre of mass remains constant.

Answer 2

Given :

Two particles of mass 5kg and 10kg respectively are attached to the two ends of a rigid rod of length 1m with negligible mass.

To Find :

The centre of mass of the system from the 5kg particle.

Solution :

❖ Centre of mass is an Imaginary point where the whole mass of system can be assumed to be concentrated.

The position of the centre of mass of a two particle system is

$\dag\:\underline{\boxed{\bf{\orange{x_{CM}=\dfrac{m_1x_1+m_2x_2}{m_1+m_2)}}}}}$

By substituting the given values;

$\sf:\implies\:x_{CM}=\dfrac{(5)(0)+(10)(1)}{5+10}$

$\sf:\implies\:x_{CM}=\dfrac{0+10}{15}$

$\sf:\implies\:x_{CM}=\dfrac{10}{15}$

$:\implies\:\underline{\boxed{\bf{\purple{x_{CM}=0.67\:m=67\:cm}}}}$

∴ (2} is the correct answer!

Knowledge BoosteR :

In rigid body, the distances between all pairs of particles do not change.

The centre of mass of an object need not lie within the object.

When the total external force on the system is zero, the velocity of the centre of mass remains constant.