Two projectiles are projected… - JEE Main 2026 Physics PYQ

JEE Main 2026 — Physics Mechanics

2026mcqmedium

Two projectiles are projected with the same initial velocities at the $15^\circ$ and $30^\circ$ with respect to the horizontal. The ratio of their ranges is $1:x$ . The value of $x$ is:

Official previous-year question

Held on 4 Apr 2026 · Verified 6 Jul 2026.

Options

A
$\sqrt{2}$
B
$\sqrt{3}$
C
$2\sqrt{3}$
D
$\dfrac{1}{\sqrt{2}}$

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Solution

The horizontal range of a projectile is given by the formula $R = \dfrac{u^2 \sin(2\theta)}{g}$ .

For the first projectile, the angle of projection is $\theta_1 = 15^\circ$ .

$R_1 = \dfrac{u^2 \sin(2 \times 15^\circ)}{g} = \dfrac{u^2 \sin(30^\circ)}{g} = \dfrac{u^2}{2g}$

For the second projectile, the angle of projection is $\theta_2 = 30^\circ$ .

$R_2 = \dfrac{u^2 \sin(2 \times 30^\circ)}{g} = \dfrac{u^2 \sin(60^\circ)}{g} = \dfrac{\sqrt{3}u^2}{2g}$

The ratio of their ranges is:

$\dfrac{R_1}{R_2} = \dfrac{\dfrac{u^2}{2g}}{\dfrac{\sqrt{3}u^2}{2g}} = \dfrac{1}{\sqrt{3}}$

Given that the ratio is $1:x$ , we get $x = \sqrt{3}$ .

Answer: $\sqrt{3}$

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Solution

The horizontal range of a projectile is given by the formula $R = \dfrac{u^2 \sin(2\theta)}{g}$ .

For the first projectile, the angle of projection is $\theta_1 = 15^\circ$ .

$R_1 = \dfrac{u^2 \sin(2 \times 15^\circ)}{g} = \dfrac{u^2 \sin(30^\circ)}{g} = \dfrac{u^2}{2g}$

For the second projectile, the angle of projection is $\theta_2 = 30^\circ$ .

$R_2 = \dfrac{u^2 \sin(2 \times 30^\circ)}{g} = \dfrac{u^2 \sin(60^\circ)}{g} = \dfrac{\sqrt{3}u^2}{2g}$

The ratio of their ranges is:

$\dfrac{R_1}{R_2} = \dfrac{\dfrac{u^2}{2g}}{\dfrac{\sqrt{3}u^2}{2g}} = \dfrac{1}{\sqrt{3}}$

Given that the ratio is $1:x$ , we get $x = \sqrt{3}$ .

Answer: $\sqrt{3}$

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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