Home
Class 11
PHYSICS
A body of mass m=10^(-2) kg is moving i...

A body of mass `m=10^(-2) kg` is moving in a medium and experiences a frictional force `F=-Kupsilon^(2).` Its initial speed is `upsilon_(0)=10ms^(-2)`. If , after `10s`, its energy is `(1)/(8)m upsilon_(0)^(2)`, the value of `k` will be

A

`10^(-1) kg m^(-1) s^(-1)`

B

`10^(-3) kg m^(-1)`

C

`10^(-3) kg s^(-1)`

D

`10^(-4) kg m^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
`F= -kv^(2)`
`m(dv)/(dt)= -kv^(2)`
`underset(v_(0))overset(v)int v^(-2) dv= underset(0)overset(t)int - (k)/(m)d t`
After 10 second, `KE= (1)/(2) mv^(2)= (1)/(8) mv_(0)^(2)`
`rArr v= (v_(0))/(2)`
`rArr [-(1)/(v)]_(v_(0))^(v_(0)//2) = - (k)/(m)t`
`rArr ((2)/(v_(0))- (1)/(v_(0))) = (k)/(m) t rArr k= (m)/(v_(0)t)= (10^(-2))/(10 xx 10)`
`k= 10^(-4) kg m^(-1)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A body of mass m = 1 kg is moving in a medium and experiences a frictional force F = -kv, where v is the speed of the body. The initial speed is v_(0) = 10 ms^(-1) and after 10 s, its energy becomes half of the initial energy. Then, the value of k is

A body of mass 10 kg is being acted upon by a force 3t^2 and an opposing constant force of 32 N. The initial speed is 10 ms^-1. The velocity of body after 5 s is

A body of mass 10 kg is moving in a circle of radian 1 m with an angular velocity of 2 rad//s the centripetal force is

A particle is moving on a straight line with constant retardation of 1 m//s^(2) . Its initial velocity is 10 m//s .

A body starts moving with a velocity v_0 = 10 ms^-1. It experiences a retardation equal to 0.2v^2. Its velocity after 2s is given by

A body of mass 1.0 kg is falling with an acceleration of 10 m//s^(2) . Its apparent weight will be (g=10m//sec^(2))

A body of mass 10 kg is upon by a force given by equation F=(3t^(2)-30) newtons. The initial velocity of the body is 10 m/s. The velocity of the body after 5 sec. is

A block of mass 2.00 kg moving at a speed of 10.0 m/s accelerates at 3.0 m/s^2 for 5.00 s. Compute its final kinetic enegy.

A body of mass 10 kg is pulled with a time varying horizontal force F=2t^(2) N on a rough surface having friction coefficient mu=0.2 . Find the speed of block after 6 seconds.