The figure shows a smooth inclined plane of inclination θ fixed in a car. A sphere is set in pure rolling on the incline. For what value of the acceleration of the car in the horizontal direction the sphere will continue pure rolling?

Question

The figure shows a smooth inclined plane of inclination θ fixed in a car. A sphere is set in pure rolling on the incline. For what value of the acceleration of the car in the horizontal direction the sphere will continue pure rolling? <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-c4de4dsyy7bqalwt.jpg" /> (A) g cos θ  (B) g sin θ  (C) g cot θ  (D) g tan θ

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-c4de4dsyy7bq3t2l.jpg" /> The sphere will continue pure rolling if ma cos θ = mg sin ⁡ θ or a=g tan θ

Q. The figure shows a smooth inclined plane of inclination $θ$ fixed in a car. A sphere is set in pure rolling on the incline. For what value of the acceleration of the car in the horizontal direction the sphere will continue pure rolling?

$g cos θ$

$g sin θ$

$g cot θ$

$g tan θ$

The sphere will continue pure rolling if
$ma cos θ = m g sin θ$
or $a = g tan θ$

Q. The figure shows a smooth inclined plane of inclination θ fixed in a car. A sphere is set in pure rolling on the incline. For what value of the acceleration of the car in the horizontal direction the sphere will continue pure rolling?

gcosθ

gsinθ

gcotθ

gtanθ