Home
Class 11
PHYSICS
A point particle of mass 0.5 kg is movin...

A point particle of mass 0.5 kg is moving along the x-axis under a force described by the potential energy V shown below. It is projected towards the right from the origin with a speed v. What is the minimum value of v for which the particle will escape infinitely fasr away from the origin ?

A

`2sqrt2ms^(-1)`

B

`2ms^(-1)`

C

`4ms^(-1)`

D

The particle will never escape

Text Solution

Verified by Experts

The correct Answer is:
A
`1/2mv^2+0=0+2rArrv=2sqrt2m//s`
Promotional Banner

Similar Questions

Explore conceptually related problems

A particle of mass m = 1.0 kg is free to move along the x axis. It is acted upon by a force which is described by the potential energy function represented in the graph below. The particle is projected towards left with a speed v, from the origin. Find minimum value of v for which the particle will escape far away from the origin.

A uniform magnetic field barB =B_(0)hatj exists in a space. A particle of mass m and charge q is projected towards negative x-axis with speed v from the a point (d,0,0) The maximum value v for which the particle does not hit y-z plane is .

A uniform magnetic field B=B_(0)hatj exists in space. A particle of mass m and charge q is projected towards X-axis with speed v from a point (a,0, 0). The maximum value of v for which the particle does not hit the Y-Z plane is

A particle of mass m=5 kg is moving with a uniform speed v=3 sqrt(2) in the XOY plane along the line Y=X+4 . The magnitude of the angular momentum of the particle about the origin is

A particle of mass 1.5 kg moves along x-axis in a conservative force field. Its potential energy is given by V(x)=2x^(3)-9x^(2)+12x, where all quantities are written in SI units. The plot of this potential energy is given below. It is seen that the particle can be in stable equilibrium at a point on x-axis, x_(0). When it is displaced slightly from this equilibrium position, It executes SHM with time period T. What is the value of x_(0) ?

A particle of mass 1.5 kg moves along x-axis in a conservative force field. Its potential energy is given by V(x)=2x^(3)-9x^(2)+12x, where all quantities are written in SI units. The plot of this potential energy is given below. It is seen that the particle can be in stable equilibrium at a point on x-axis, x_(0). When it is displaced slightly from this equilibrium position, It executes SHM with time period T. What is the time period of SHM mentioned in the paragraph?

A particle of mass m moves on positive x-axis under the influence of force acting towards the origin given by -kx^2 hat i. If the particle starts from rest at x=a, the speed it will attain when it crosses the origin is