Question

If a particle takes $t$ second less and acquires a velocity of $v \,m/s$ more in falling through the same distance on two planets where the accelerations due to gravity are $2\,g$ and $8\,g$ respectively then

• A. v = 4 gt
• B. v = 5 gt
• C. v = 2 gt
• D. v = 16 gr

Answer 1

Answer: (A)

$\frac{v}{t}=\frac{v_{1}-v_{2}}{t_{2}-t_{1}}$
$=\frac{\sqrt{2 a_{1} s}-\sqrt{2 a_{2} s}}{\sqrt{\frac{2 s}{a_{2}}}-\sqrt{\frac{2 s}{a_{1}}}}$
$ \Rightarrow v=\left(\sqrt{a_{1} a_{2}}\right) t $
$\Rightarrow v=\sqrt{(2 g)}(8 g) t $
$\Rightarrow v=\sqrt{16 g^{2} t} $
$\Rightarrow v=4 \,g t$