Question

52. A balloon with mass ‘m’ is descending down with an acceleration ‘a’ (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration ‘a’? (1) 2ma g a + (2) 2ma g a - (3) ma g a + (4) ma g a - 53.​

Answer 1

Refer the attachment ❤️

Answer 2

Explanation:

Initially, the balloon of mass m is descending down with acceleration a (where a < g) [ refer to the diagram in the attachment for better understanding!]

The net force acting on the balloon,

⇒ mg - F = ma

⇒ F = mg - ma ....(1)

Now we need to find the amount of mass removed for the balloon to move up with acceleration a

Let the amount of mass removed be m'

The net mass of the balloon,

⇒ m ₙₑₜ = m - m'

Now, the net force acting on the balloon,

⇒ F - m ₙₑₜ g = mₙₑₜ a

⇒ F - (m-m') g = (m-m') a

⇒ F = ma - m'a + mg - m'g ....(2)

From eq (1) and (2) we get,

⇒ mg - ma = ma - m'a + mg - m'g

⇒ m'g + m'a = ma + mg - mg + ma

⇒ m'(g + a ) = 2ma

$\to \boxed{\sf {m' =\dfrac{ 2ma }{g + a} }}$