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A small cart with a sphere suspended fro...

A small cart with a sphere suspended from ceiling by a string is moving up an inclined plane at a constant speed V. The direction of string supporting the sphere is `:`

A

vertical

B

horizontal

C

perpendicular to the inclined plane

D

none of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, let's analyze the situation step by step. ### Step 1: Understand the System We have a small cart that is moving up an inclined plane at a constant speed \( V \). A sphere is suspended from the ceiling of the cart by a string. **Hint:** Identify the forces acting on the sphere and the motion of the cart. ### Step 2: Analyze the Forces on the Sphere When the cart is moving up the incline at a constant speed, the forces acting on the sphere are: - The gravitational force acting downwards (weight of the sphere, \( mg \)). - The tension in the string acting upwards. **Hint:** Remember that the gravitational force is always directed downwards towards the center of the Earth. ### Step 3: Consider the Motion of the Cart Since the cart is moving at a constant speed, there is no net acceleration acting on the cart or the sphere. This means that the forces acting on the sphere must be balanced. **Hint:** Use Newton's first law of motion which states that an object at rest or moving at constant velocity will remain in that state unless acted upon by a net external force. ### Step 4: Determine the Orientation of the String As the cart moves up the incline, the tension in the string must balance the weight of the sphere. Since there is no acceleration, the tension will act vertically upwards to counteract the weight of the sphere acting downwards. **Hint:** Visualize the forces: the tension in the string must be equal to the weight of the sphere for the sphere to remain in equilibrium. ### Step 5: Conclusion Since the only forces acting on the sphere are the weight acting downwards and the tension acting upwards, and there is no net force acting in the horizontal direction (due to constant speed), the string remains vertical. **Final Answer:** The direction of the string supporting the sphere is vertical.
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