Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls when in air

Question

Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls when in air (A) is equal to g (acceleration due to gravity) (B) depends in the speeds of the two balls (C) depends on the masses of the two balls (D) depends on the direction of motion of the two balls.

Tardigrade Admin · Accepted Answer

We know that,
Acceleration of centre of mass

a_{c m} = \frac{m _{1} a _{1} + m _{2} a _{2}}{m _{1} + m _{2}}

Here,

a_{1} = a_{2} = g

(Because balls are thrown in air i.e. under the gravity)

a_{c m} = \frac{m _{1} g + m _{2} g}{m _{1} + m _{2}}

a_{c m} = \frac{g ( m _{1} + m _{2} )}{m _{1} + m _{2}}

a_{c m} = g

Q. Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls when in air

is equal to $g$ (acceleration due to gravity)

depends in the speeds of the two balls

depends on the masses of the two balls

depends on the direction of motion of the two balls.

Q. Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls when in air

is equal to g (acceleration due to gravity)

depends in the speeds of the two balls

depends on the masses of the two balls

depends on the direction of motion of the two balls.

We know that, Acceleration of centre of mass acm​=m1​+m2​m1​a1​+m2​a2​​ Here, a1​=a2​=g (Because balls are thrown in air i.e. under the gravity) acm​=m1​+m2​m1​g+m2​g​ acm​=m1​+m2​g(m1​+m2​)​ acm​=g

is equal to $g$ (acceleration due to gravity)