Question

Assertion :A body is dropped form height $h$ and another body is thrown vertically upwards with a speed $\sqrt{gh}.$ They meet at height $\frac{h}{2}$. Reason: The time taken by both the blocks in reaching the height $\frac{h}{2}$ is same.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
• C. Assertion is correct but Reason is incorrect.
• D. Both Assertion is incorrect but Reason is correct.

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

initially the separation between the two bodies is h therefore

$S_1=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}g{t}^2$

$S_2=\sqrt{gh}t-\frac{1}{2}g{t}^2$

$S_1+S_2=h$

$\sqrt{gh}t=h$

$t=\sqrt{\frac{h}{g}}$

$S_1=\frac{1}{2}g(\sqrt{\frac{h}{g}}{)}^2=\frac{h}{2}$

$S_2=\frac{h}{2}$