An object is shot from the bottom of a smooth inclined plane at 60° with the horizontal and travels distance x_1 along the plane. When the inclination is reduced to 30° and the object is shot with the same speed, it travels x_2. The ratio x_1 : x_2 is:

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NEET Physics QUESTION #7293

Question 1

An object is shot from the bottom of a smooth inclined plane at $60°$ with the horizontal and travels distance $x_1$ along the plane. When the inclination is reduced to $30°$ and the object is shot with the same speed, it travels $x_2$. The ratio $x_1 : x_2$ is:

$1:\sqrt{2}$
$\sqrt{2}:1$
$1:\sqrt{3}$✔️
$1:2\sqrt{3}$

Correct Answer Explanation

For a projectile launched along a smooth inclined plane, the range along the incline is: $x = \dfrac{2u^2\sin(\theta-\alpha)\cos\theta}{g\cos^2\alpha}$, where $\alpha$ is the incline angle and $\theta$ the launch angle from horizontal.

When the projectile is fired along the incline: $\theta = \alpha$, so $\sin(\theta-\alpha) = 0$... Using the general formula and applying both cases gives $x_1 : x_2 = \mathbf{1:\sqrt{3}}$.

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