Question

A balloon initially at rest start rising with constant acceleration of $10{\text{m/s}}^2$. After $2\text{s}$ a particle drops from the balloon. After further $2\text{s}$, match the following (Take $g=10{\text{m/s}}^2$ )
$\begin{array}{cc}\text{Table-1}& \text{Table-2}\\ \text{(A) Height of particle from ground is}& \text{(P) Zero}\\ \text{(B) Speed of particle is}& \text{(Q) 10 SI units}\\ \text{(C) Displacement of particle is}& \text{(R) 40 SI units}\\ \text{(D) Acceleration of particle is}& \text{(S) 20 SI units}\end{array}$

• A. $\left(A\right)\to \left(R\right);\left(B\right)\to \left(P\right);\left(C\right)\to \left(S\right);\left(D\right)\to \left(Q\right)$
• B. $\left(A\right)\to \left(R\right);\left(B\right)\to \left(Q\right);\left(C\right)\to \left(P\right);\left(D\right)\to \left(S\right)$
• C. $\left(A\right)\to \left(S\right);\left(B\right)\to \left(P\right);\left(C\right)\to \left(R\right);\left(D\right)\to \left(Q\right)$
• D. $\left(A\right)\to \left(S\right);\left(B\right)\to \left(Q\right);\left(C\right)\to \left(R\right);\left(D\right)\to \left(P\right)$

Answer 1

The correct option is A $\left(A\right)\to \left(R\right);\left(B\right)\to \left(P\right);\left(C\right)\to \left(S\right);\left(D\right)\to \left(Q\right)$

Height of the balloon after $t=2\text{s}$ is given by
$S_1=ut+\frac{1}{2}\left(10\right)2^2$
As the initial velocity of balloon is $0$
$\Rightarrow S_1=+20\text{m}$
Velocity of balloon after $t=2\text{s}$ is
$v=0+20=+20\text{m/s}$ (Take upward direction as positive)
When the particle is dropped, its initial velocity $=+20\text{m/s}$
After further $2\text{s}$, the displacement of the particle is
$S_2=20\times 2-\frac{1}{2}\times 10\times 2^2$
$\Rightarrow S_2=20\text{m}$
Thus height of the particle from ground, $S_1+S_2=40\text{m}$
Speed of the particle after further $2\text{s},v_2=20-10\left(2\right)$
$\Rightarrow v_2=0$
Since the velocity becomes zero after further $2s$, therefore the particle starts falling freely and hencce the acceleration will act due to graity i.e. $10{\text{m/s}}^2$.