Question

A balloon of mass 60 g is moving up with an acceleration of 4 m/s\(^2\). The mass to be added to the balloon to descend it down with the same acceleration is (g = 10 m/s\(^2\)):

• A. 60 g
• B. 80 g
• C. 100 g
• D. 120 g
• E. 40 g

Hint:

For an object moving upward or downward, the net force required is the difference between the force of gravity and the force of acceleration. To reverse the direction while maintaining the same acceleration, add an appropriate mass to achieve the desired net force.

Answer 1

The Correct Option is B

Let the mass of the balloon be \( m = 60 \, {g} = 0.06 \, {kg} \).
When the balloon is moving upward with an acceleration of \( 4 \, {m/s}^2 \), the net force on the balloon is given by Newton’s second law: \[ F_{{net}} = m a \] where: - \( m = 0.06 \, {kg} \) is the mass of the balloon - \( a = 4 \, {m/s}^2 \) is the upward acceleration. 
The upward force is: \[ F_{{up}} = m(g + a) = 0.06 \times (10 + 4) = 0.06 \times 14 = 0.84 \, {N} \] Now, to make the balloon move downward with the same acceleration, we need to add a mass to it, and the net force should be in the downward direction. For the downward motion, the net force is: \[ F_{{net}} = (m + M) \times a \] where \( M \) is the additional mass to be added. The downward force needed to get the balloon to descend with the same acceleration is equal to the force required to accelerate the added mass: \[ (m + M)(g - a) = F_{{up}} \quad \Rightarrow \quad (0.06 + M)(10 - 4) = 0.84 \] \[ (0.06 + M)(6) = 0.84 \] \[ 0.06 + M = \frac{0.84}{6} = 0.14 \] \[ M = 0.14 - 0.06 = 0.08 \, {kg} = 80 \, {g} \] Thus, the mass to be added to the balloon to make it descend with the same acceleration is \( 80 \, {g} \). \[ \boxed{80 \, {g}} \]