Question

Assertion :The maximum height reached by an object projected vertically up is directly proportional to the initial velocity u. Reason: The maximum height reached by an object thrown up with an initial velocity u is given by $h=\frac{u^2}{2g}$.

• 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. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Initial velocity of the object is $u$.

Acceleration due to gravity acting on the object is $a=-g$

At maximum height $\left(h\right)$ attained, velocity of the object is zero i.e. $v=0$

Using $v^2-u^2=2ah$

Or $0-u^2=2(-g)h$

$⟹$ $h=\frac{u^2}{2g}$

Thus we get $h\propto u^2$

So, maximum height attained is directly proportional to the square of the initial velocity.

Hence the reason statement is correct but the assertion statement is incorrect.