(D) The velocity of the centre of mass $(v_{cm})$ for a system of particles is given by the formula:$v_{cm} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}$Give

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(D) The velocity of the centre of mass $(v_{cm})$ for a system of particles is given by the formula:$v_{cm} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}$Given:Mass of the first block $(m_1)$ = $5 \,kg$Velocity of the first block $(v_1)$ = $7 \,m/s$Mass of the second block $(m_2)$ = $2 \,kg$Velocity of the second block $(v_2)$ = $0 \,m/s$ (initially at rest)Substituting the values into the formula:$v_{cm} = \frac{5 \times 7 + 2 \times 0}{5 + 2}$$v_{cm} = \frac{35 + 0}{7}$$v_{cm} = \frac{35}{7} = 5 \,m/s$Therefore,the velocity of the centre of mass is $5 \,m/s$.

Class 11 Physics System of Particles and Rotational Motion Motion of Centre of Mass

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Two blocks of masses $5 \,kg$ and $2 \,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $7 \,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ....... $m/s$.

A
$30$
B
$20$
C
$10$
D
$5$

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System of Particles and Rotational Motion

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Motion of Centre of Mass

Two spherical objects have masses $M$ and $5M$ and radii $R$ and $2R$ respectively. They are released in free space with their centers at a distance of $12R$. If they attract each other only due to gravitational force,the distance traveled by the smaller object before collision is: (in $R$)

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$A$ particle of mass $m$ is thrown horizontally from the top of a tower and another particle of mass $2m$ is thrown vertically upward. The acceleration of the centre of mass is .............

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Two skaters $A$ and $B$ of weights in the ratio $5 : 7$ start facing each other $6\,m$ apart on a horizontal smooth surface. They pull on a rope stretched between them. How far has each moved when they meet?

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$A$ body of mass $2 \,kg$ is moving towards north with a velocity of $20 \,m \,s^{-1}$ and another body of mass $3 \,kg$ is moving towards east with a velocity of $10 \,m \,s^{-1}$. The magnitude of the velocity of the centre of mass of the system of the two bodies is

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Two men of masses $55 \ kg$ and $65 \ kg$ are standing at the opposite ends of a boat. The length of the boat is $3.0 \ m$ and its mass is $100 \ kg$. The $55 \ kg$ man walks up to the $65 \ kg$ man and sits beside him. If the boat is in still water,the center of mass of the system will shift by ..... $m$.

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Two blocks of masses $5 \,kg$ and $2 \,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $7 \,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ....... $m/s$.

Similar Questions

Two spherical objects have masses $M$ and $5M$ and radii $R$ and $2R$ respectively. They are released in free space with their centers at a distance of $12R$. If they attract each other only due to gravitational force,the distance traveled by the smaller object before collision is: (in $R$)

$A$ particle of mass $m$ is thrown horizontally from the top of a tower and another particle of mass $2m$ is thrown vertically upward. The acceleration of the centre of mass is .............

Two skaters $A$ and $B$ of weights in the ratio $5 : 7$ start facing each other $6\,m$ apart on a horizontal smooth surface. They pull on a rope stretched between them. How far has each moved when they meet?

$A$ body of mass $2 \,kg$ is moving towards north with a velocity of $20 \,m \,s^{-1}$ and another body of mass $3 \,kg$ is moving towards east with a velocity of $10 \,m \,s^{-1}$. The magnitude of the velocity of the centre of mass of the system of the two bodies is

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