JEE Mains · Physics · STD 11 - 4.1 newtons laws of motion
A balloon and its content having mass \(M\) is moving up with an acceleration ' \(a\) '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' \(3 a^{\prime}\) will be
(Take ' g ' as acceleration due to gravity)
- A \(\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}\)
- B \(\frac{3 \mathrm{Ma}}{2 \mathrm{a}-\mathrm{g}}\)
- C \(\frac{3 \mathrm{Ma}}{2 \mathrm{a}+\mathrm{g}}\)
- D \(\frac{2 \mathrm{Ma}}{3 \mathrm{a}-\mathrm{g}}\)
Answer & Solution
Correct Answer
(A) \(\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & F-m g=m a \\ & F=m a+m g \\ & F-(m-x) g=(m-x) 3 a \end{aligned}\) Put F \(\begin{aligned} & \mathrm{Ma}+\mathrm{mg}-\mathrm{mg}+\mathrm{xg}=3 \mathrm{ma}-3 \mathrm{xa} \\ & \mathrm{x}=\frac{2 \mathrm{ma}}{\mathrm{~g}+3 \mathrm{a}} \end{aligned}\)
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