Home
Class 11
PHYSICS
A smooth rope of mas m and length L lies...

A smooth rope of mas `m` and length `L` lies in a heap on a smooth horizontal floor, with one end attached to a block of mass `M`. The block is given a sudden kick and instantaneously acquires a horizontal velocity of magnitude `V_(0)` as shown in figure 1. As the block moves to right pulling the rope from heap, the rope being smooth, the heap remains at rest. At the instant block is at a distance `x` from point `P` as shown in figure `-2( P` is a point on the rope which has just started to move at the given instant `)`, choose correct options for next three question.

The tension in rope at point `P` is

A

`(mM^(2))/(L)(V_(0)^(2))/((M+(m)/(L)x)^(2))`

B

`(m^(2)M)/(L)(V_(0)^(2))/((M+(m)/(L)x)^(2))`

C

`(m^(3))/(L)(V_(0)^(2))/((M+(m)/(L)x)^(2))`

D

`(M^(3))/(L)(V_(0)^(2))/((M+(m)/(L)x)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
The mass of moving material is `M+(m)/(L)x`
From conservation of momentum `MV_(0)=(M+(m)/(L)x)V`
`:. `Velocity of moving block and moving rope is
`V=(MV_(0))/(M+(m)/(L)x)`
`(A)` The tension at point `P` is what give momentume to next tiny piece `(` to left of `P )` that starts moving . The speed of this piece increases from 0 to `V` in time `dt.`
`rArr dp =dmV`
`or F=(dP)/(dt)=(dm)/(dt)V=((m)/(L)dx)/(dt)V=(m)/(L)V^(2)`
`:. F_(P)=(m)/(L)(M^(2)V_(0)^(2))/((M+(m)/(L)x)^(2))`
Promotional Banner

Similar Questions

Explore conceptually related problems

A smooth rope of mas m and length L lies in a heap on a smooth horizontal floor, with one end attached to a block of mass M . The block is given a sudden kick and instantaneously acquires a horizontal velocity of magnitude V_(0) as shown in figure 1. As the block moves to right pulling the rope from heap, the rope being smooth, the heap remains at rest. At the instant block is at a distance x from point P as shown in figure -2( P is a point on the rope which has just started to move at the given instant ) , choose correct options for next three question. The speed of block of mass M is

A smooth rope of mas m and length L lies in a heap on a smooth horizontal floor, with one end attached to a block of mass M . The block is given a sudden kick and instantaneously acquires a horizontal velocity of magnitude V_(0) as shown in figure 1. As the block moves to right pulling the rope from heap, the rope being smooth, the heap remains at rest. At the instant block is at a distance x from point P as shown in figure -2( P is a point on the rope which has just started to move at the given instant ) , choose correct options for next three question. The magnitude of acceleration of block of mass M is

If A block is dragged on a smooth horizontal plane with the help of a light rope which moves with a velocity v as given in the figure .Then find the horizontal velocity of the block .

A long block A is at rest on a smooth horizontal surface. A small block B whose mass is half of mass of A is placed on A at one end and is given an initial velocity u as shown in figure. The coefficient of friction between the blocks is mu .

A uniform rope of mass m and length L is attached to the ceiling of a lift. The other end of the rope is attached to a block of mass M . The lift is moving up with a constant acceleration a_(0) . Find the tension in the rope at a distance x from the ceiling as shown in the diagram.

A block of mass m rests on a stationary wedge of mass M. The wedge can slide freely on a smooth horizontal surface as shown in figure. If the block starts from rest

A block is dragged on a smooth plane with the help of a rope which moves with a velocity v as shown in figure. The horizontal velocity of the block is :

A block of mass 20 kg is set into motion on a frictionless horizontal surface with the help of massless smooth pulley and rope as shown in the figure. Find the acceleration of the pulley

A block of mass m, attacted to a string of spring constant k, oscillates on a smooth horizontal table. The other end of the spring is fixed to a wall. The block has a speed v when the spring is at its natural length. Before coming to an instantaneous rest. If the block moves a distance x from the mean position, then

A wooden block of mass m resting on a rough horizontal table (coefficient of friction = mu ) is pulled by a force F as shown in figure.The acceleration of the block moving horizontally is :