
A yo-yo is resting on a perfectly rough horizontal table. Now, forces , and are applied separately as shown in the figure below. Assume that the horizontal component of the force is less than the kinetic friction. Then the correct statement is:
A) When is applied to the centre of mass moves to the right.
B) When is applied to the centre of mass moves to the left.
C) When is applied to the centre of mass moves to the right.
D) When is applied to the centre of mass moves to the right.

Answer
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Hint:The centre of mass of the yo-yo paced on the horizontal surface when a force is applied to it. The direction of motion of the centre of mass will along the direction of the force applied. Here, out of the three forces applied to the yo-yo, only the force contributes to the movement of the yo-yo towards the right.
Complete step by step answer.
Step 1: Describe the effect on the centre of mass of the yo-yo when force is applied.
The force is directed towards the right. When the force is applied on the yo-yo, placed on the horizontal surface, the yo-yo moves along the direction of i.e., towards the right.
Therefore, on the application of the force the centre of mass of the yo-yo moves to the right.
Step 2: Describe the effect on the centre of mass of the yo-yo when force is applied.
To explain the effect of the force on the yo-yo, we first resolve into its horizontal and vertical components, i.e. and .
Here, only the horizontal component of contributes in the movement of the yo-yo towards the right or left. But it is given that the horizontal component is less than the kinetic friction. This means that the horizontal component will not cause the centre of mass to move towards the right or left.
Step 3: Describe the effect on the centre of mass of the yo-yo when force is applied.
The force acts vertically upwards. This can only cause the yo-yo to move upwards. Thus when is applied to the yo-yo, the centre of mass of the yo-yo cannot move towards the right.
Therefore, we can conclude that when force is applied, the centre of mass moves to the right.
Note: The surface on which the yo-yo resides is described as a perfectly rough horizontal surface. This implies that frictional forces are evident. When force was applied the yo-yo did not move. As mentioned before, this was because the horizontal component of was lesser than the kinetic friction i.e., the horizontal component of wasn’t strong enough to overcome the frictional force to produce an observable movement of the yo-yo.
Complete step by step answer.
Step 1: Describe the effect on the centre of mass of the yo-yo when force
The force
Therefore, on the application of the force
Step 2: Describe the effect on the centre of mass of the yo-yo when force
To explain the effect of the force

Here, only the horizontal component of
Step 3: Describe the effect on the centre of mass of the yo-yo when force
The force
Therefore, we can conclude that when force
Note: The surface on which the yo-yo resides is described as a perfectly rough horizontal surface. This implies that frictional forces are evident. When force
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