Question

As shown in figure, a yo-yo is at rest on a frictionless surface. When a force $F$ applied in string as shown in fig., the yo-yo:

A) moves to the left and rotates anti-clockwise.
B) moves to the right and rotates anti-clockwise.
C) moves to the left and rotates clockwise.
D) moves to the right and rotates clockwise.

Answer 1

An object is moved in the direction of net force applied on the object. Similarly it rotates in the direction of net torque applied on the object. Here the surface is frictionless hence only force $F$ is responsible for movement of yo-yo.

Complete step by step answer:

In the given diagram, F is the only force applied on yo-yo in the right direction. So, yo-yo moves in the right direction.
To find rotation we need to find torque applied on yo-yo by the force $F$. Torque on yo-yo is given by
$\vec \tau = \vec r \times \vec F$
where $F$ is force applied and $r$ is perpendicular distance between the centre of rotation and the applied force.
As shown in figure, there is only force $F$ which is applied on yo-yo and the torque due to force $F$ rotate the yo-yo in an anti-clockwise direction.
Then, the yo-yo moves in the right direction and rotates in an anti-clockwise direction.
Hence, the correct answer is option B.

Note: If the ground surface has friction, then the direction of force remains the same but the direction of torque may change due to friction force. If the direction of torque changes then the direction of rotation also changes. Means if friction is present our answer may be different or same depending on coefficient of friction between the yo-yo and plane surface.