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A yo-yo is resting on a perfectly rough horizontal table. Now, forces F1 , F2 and F3 are applied separately as shown in the figure below. Assume that the horizontal component of the force F2 is less than the kinetic friction. Then the correct statement is:
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A) When F3 is applied to the centre of mass moves to the right.
B) When F2 is applied to the centre of mass moves to the left.
C) When F1 is applied to the centre of mass moves to the right.
D) When F1 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 F1 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 F1 is applied.
The force F1 is directed towards the right. When the force F1 is applied on the yo-yo, placed on the horizontal surface, the yo-yo moves along the direction of F1 i.e., towards the right.
Therefore, on the application of the force F1 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 F2 is applied.
To explain the effect of the force F2 on the yo-yo, we first resolve F2 into its horizontal and vertical components, i.e. F2cosθ and F2sinθ .
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Here, only the horizontal component of F2 contributes in the movement of the yo-yo towards the right or left. But it is given that the horizontal component F2sinθ is less than the kinetic friction. This means that the horizontal component F2sinθ 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 F3 is applied.
The force F3 acts vertically upwards. This can only cause the yo-yo to move upwards. Thus when F3 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 F1 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 F2 was applied the yo-yo did not move. As mentioned before, this was because the horizontal component of F2 was lesser than the kinetic friction i.e., the horizontal component of F2 wasn’t strong enough to overcome the frictional force to produce an observable movement of the yo-yo.