JEE Main 2022 · 25 Jun · Shift 2 · Physics Q31

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PhysicsSingle correct+4 / -1Question 31 of 90

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Two identical balls $A$ and $B$ thrown with same velocity ' $u$ ' at two different angles with horizontal attained the same range $R$ . If $A$ and $B$ reached the maximum height $h_1$ and $h_2$ respectively, then $R=4\sqrt{h_1h_2}$

Reason R: Product of said heights.
$h_1h_2=\left(\frac{u^2\sin^2\theta}{2g}\right)\cdot\left(\frac{u^2\cos^2\theta}{2g}\right)$
Choose the correct answer :

Both A and R are true and R is the correct explanation of A.

Both A and R are true but R is NOT the correct explanation of A.

A is true but R is false.

A is false but R is true.

Answer and worked solution

Official answer: A

Same range at speed $u$ means complementary angles $\theta$ and $90°-\theta$ , so $h_1=\dfrac{u^2\sin^2\theta}{2g}$ and $h_2=\dfrac{u^2\cos^2\theta}{2g}$ (R is true).

Then $\sqrt{h_1h_2}=\dfrac{u^2\sin\theta\cos\theta}{2g}=\dfrac R4$ , so $R=4\sqrt{h_1h_2}$ (A is true, and follows from R).

(A)

Topics:Projectile motion

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JEE Main 2022 · 25 Jun · Shift 2, Physics question 31