Home
Class 12
PHYSICS
A solid sphere of radius R is placed on ...

A solid sphere of radius `R` is placed on a smooth horizontal surface. A horizontal force `F` is applied at height `h` from the lowest point. For the maximum acceleration of the centre of mass

A

`h=R`

B

`h=2R`

C

`h=0`

D

the acceleration will be same whatever `h` may be

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of determining the maximum acceleration of the center of mass of a solid sphere when a horizontal force \( F \) is applied at a height \( h \) from the lowest point, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the System**: - We have a solid sphere of radius \( R \) resting on a smooth horizontal surface. - A horizontal force \( F \) is applied at a height \( h \) from the lowest point of the sphere. 2. **Identify the Forces**: - The only external horizontal force acting on the sphere is \( F \). - The sphere has a mass \( m \). 3. **Acceleration of the Center of Mass**: - The acceleration \( a_{cm} \) of the center of mass of the sphere can be calculated using Newton's second law: \[ a_{cm} = \frac{F}{m} \] - This equation indicates that the acceleration of the center of mass depends solely on the net external force \( F \) and the mass \( m \) of the sphere. 4. **Effect of Height \( h \)**: - The height \( h \) at which the force is applied affects the torque about the center of mass but does not affect the linear acceleration of the center of mass. - The torque \( \tau \) caused by the force \( F \) is given by: \[ \tau = F \cdot h \] - However, since the surface is smooth, the sphere will not roll, and the force will only contribute to the linear acceleration. 5. **Conclusion**: - Since the linear acceleration \( a_{cm} \) is independent of the height \( h \), we can conclude that the acceleration of the center of mass remains the same regardless of the value of \( h \). - Therefore, the correct answer is that the acceleration will be the same for any height \( h \). ### Final Answer: The correct option is \( D \): The acceleration will be the same regardless of the height \( h \).
Promotional Banner

Similar Questions

Explore conceptually related problems

A solid sphere of radius R is resting on a smooth horizontal surface. A constant force F is applied at a height h from the bottom. Choose the correct alternative.

A uniform sphere is place on a smooth horizontal surface and as horizontal force F is appied on it at a distance h above the surface. The acceleratioin of the centre

A solid sphere of mass ma nd radis R is placed on a rough horizontal surface A horizontal force F is applied to sphere at a height h, (0lehleR) from centre. If sphere rolls slipping then,

A uniform solid cylinder of mass m and radius R is placed on a rough horizontal surface. A horizontal constant force F is applied at the top point P of the cylinder so that it start pure rolling. The acceleration of the cylinder is

A sphere of mass m and radius r is placed on a rough plank of mass M . The system is placed on a smooth horizontal surface. A constant force F is applied on the plank such that the sphere rolls purely on the plank. Find the acceleration of the sphere.

Uniform solid cylinder of mass m and radius R is placed on a rough horizontal surface. A horizontal constant force is applied at the top point P of the cylinder so that it start pure rolling .In the above question, the frictional force on the cylinder is

A solid sphere rests on a horizontal surface. A horizontal impulse is applied at height h from centre. The sphere starts rolling just after the application of impulse. The ratio h//R will be

A solid sphere of mass M and radius R is placed on a rough horizontal surface. It is stuck by a horizontal cue stick at a height h above the surface. The value of h so that the sphere performs pure rolling motion immediately after it has been stuck is

A block of unknown mass is at rest on a rough, horizontal surface. A horizontal force F is applied to the block. The graph in the figure shows the acceleration of the block with respect to the applied force. The mass of the block is

A wire is wrapped N times over a solid sphere of mass m which is place on a smooth horizontal surface. A horizontal magnetic field of induction vec B is present. Find the (a) torque (b) angular acceleration experienced by the sphere. Assume that the mass of the wire is negligible compared to the mass of the sphere.