Question

A sphere is given an initial push so that it starts rolling (without slipping) up an inclined plane. During its climb

• A. the direction of the force of friction on the sphere is up the incline.
• B. the direction of the net force on the sphere is up the incline.
• C. the net torque on the sphere is zero.
• D. the work done by the force of friction on the sphere is negative.

Hint:

For a rolling body decelerating on an incline, friction always acts in the direction that helps slow down both the rotation and translation in a synchronized manner. Here, that direction is up the incline.

Answer 1

The Correct Option is A

Step 1: Set the scene.
A sphere rolls without slipping up an incline after a push. As it climbs, gravity slows it down, so it is decelerating both in speed and in spin.

Step 2: Think about what slows the spin.
Since the sphere is slowing its rotation, there must be a torque acting to reduce its spin. Gravity acts at the centre and gives no torque, so friction must supply this torque.

Step 3: Find the friction direction.
To create a torque that slows the forward spin while it moves up, the friction at the contact point must point up the incline. This is the only way to keep rolling consistent as the body decelerates.

Step 4: Check the net force direction.
Gravity's component down the slope is larger than the up-slope friction, so the net force points down the incline, which is why it decelerates. So that net-force-up claim is wrong.

Step 5: Check the torque and work claims.
The torque is clearly not zero, since the spin is changing. Static friction at a non-slipping contact point does no work, because the contact point is momentarily at rest, so the negative-work claim is also wrong.

Step 6: Pick the valid statement.
Only the statement about friction pointing up the incline survives. \[ \boxed{\text{Friction acts up the incline}} \]