Home
Class 12
PHYSICS
A particle moves in a straight line with...

A particle moves in a straight line with retardation proportional to its displacement. Its loss in kinetic energy for any displacement x is proportional to

A

X

B

`e^(x)`

C

`x^(2)`

D

`log_(e) x`

Text Solution

Verified by Experts

The correct Answer is:
C
According to problem,
Retardation displacement
or `v(dv)/(dx) = -kx " or " int_(v_1)^(v_2) vdv = -k int_(0)^(x) xdx " or " (v_2^2)/(2) - (v_1^2)/(2) = -(kx^2)/(2)`
or `1/m ((mv_1^2)/(2) - (mv_2^2)/(2)) = (kx^2)/(2) " or "(k_1 - k_2) = (mk)/2 x^2`
Thus, loss of kinetic energy is proportional to `x^2`.
Promotional Banner

Similar Questions

Explore conceptually related problems

A particle move in a straight line with retardation proportional to its displacement its loss of kinectic energy for any displacement x is proportional to

A particle moves in a straight line with retardatino proportional it its displacement. Calculate the loss of K.E. for any displacement x .

A particle moves in a straight line with acceleration proportional to x^2 , ( Where x is displacement). The gain of kinetic energy for any displacement is proportional to

A particle moves in a straight line so that s=sqrt(t) , then its acceleration is proportional to

A particle starts with speed v_(0) from x = 0 along x - axis with retardation proportional to the square of its displacement. Work done by the force acting on the particle is proportional to