A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :- A
- B
- C
- D
View written solutionFree
Correct answer: D
-
Use conservation of mechanical energy
Since the block is simply released and compresses the spring to the maximum extent, its initial gravitational potential energy becomes spring potential energy at maximum compression. -
Let the maximum compression be
If the block moves a total distance along the incline before stopping, then from the figure the vertical drop corresponding to that motion contributes to loss in gravitational potential energy. -
Energy balance
At maximum compression, velocity becomes zero, so where is the vertical drop from the initial point to the point of maximum compression. -
Using the values from the given figure
From the figure, substituting the given data into the energy equation gives -
Check options
Thus the maximum compression is which corresponds to Option D.
More from Work Power and Energy
- A particle of mass moves on a straight line with its velocity increasing with distance according to the equation , where is a constant. The total work done by all the forces applied on the particle during…2024 · MCQ
- A force displaces a body from to . Work done by this force is J.2024 · Numerical
- A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle of thread deflection in the extreme position will be :2024 · MCQ
- A bullet is fired into a fixed target looses one third of its velocity after travelling . It penetrates further before coming to rest. The value of is :2024 · MCQ
- A block of mass slides over a distance of on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction ) is :2024 · MCQ
- The potential energy function (in ) of a particle in a region of space is given as . Here and are in meter. The magnitude of -component of force (in ) acting on the particle at point …2024 · MCQ
- A bob of mass '' is suspended by a light string of length ''. It is imparted a minimum horizontal velocity at the lowest point such that it just completes half circle reaching the top most position B. The ratio of kinetic… Includes diagram2024 · MCQ
- A particle is placed at the point of a frictionless track as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is : (Take ). Includes diagram2024 · MCQ