Given below are two statements. One is… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Mechanics

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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 $R=4\sqrt{{h}_{1}{h}_{2}}$

Reason R: Product of said heights. ${h}_{1}{h}_{2}=(\frac{{u}^{2}{\mathrm{sin}}^{2}\theta }{2g})\cdot (\frac{{u}^{2}{\mathrm{cos}}^{2}\theta }{2g})$

Official previous-year question

Held on 25 Jun 2022 · Verified 6 Jul 2026.

Options

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is NOT the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

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Solution

Range of two balls are ${R}_{1}=\frac{{u}^{2}\mathrm{sin}2{\theta }_{1}}{g}={R}_{2}=\frac{{u}^{2}\mathrm{sin}2{\theta }_{2}}{g}$ .

Now, maximum height by both balls are ${h}_{1}=\frac{{u}^{2}{\mathrm{sin}}^{2}{\theta }_{1}}{2g}$ and ${h}_{2}=\frac{{u}^{2}{\mathrm{cos}}^{2}{\theta }_{2}}{2g}$

$\therefore \sqrt{{h}_{1}{h}_{2}}=(\frac{{u}^{2}{\mathrm{sin}}^{2}\theta }{2g})(\frac{{u}^{2}{\mathrm{cos}}^{2}\theta }{2g})=\frac{{u}^{2}\mathrm{sin}\theta \mathrm{cos}\theta }{2g}$ $=\frac{R}{4}$

${\Rightarrow R=4\sqrt{{h}_{1}{h}_{2}}}^{}$

Hence, both A and R are true and R is the correct explanation of A.

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Solution

Range of two balls are ${R}_{1}=\frac{{u}^{2}\mathrm{sin}2{\theta }_{1}}{g}={R}_{2}=\frac{{u}^{2}\mathrm{sin}2{\theta }_{2}}{g}$ .

Now, maximum height by both balls are ${h}_{1}=\frac{{u}^{2}{\mathrm{sin}}^{2}{\theta }_{1}}{2g}$ and ${h}_{2}=\frac{{u}^{2}{\mathrm{cos}}^{2}{\theta }_{2}}{2g}$

$\therefore \sqrt{{h}_{1}{h}_{2}}=(\frac{{u}^{2}{\mathrm{sin}}^{2}\theta }{2g})(\frac{{u}^{2}{\mathrm{cos}}^{2}\theta }{2g})=\frac{{u}^{2}\mathrm{sin}\theta \mathrm{cos}\theta }{2g}$ $=\frac{R}{4}$

${\Rightarrow R=4\sqrt{{h}_{1}{h}_{2}}}^{}$

Hence, both A and R are true and R is the correct explanation of A.

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Solution

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Options

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics