A particle of mass `m` moves along a circle of radius `R` with a normal acceleration varying with time as `a_(n) = bt^(2)`, where `b` is a constant. Find the time dependence of the power developed by all the forces acting on the particle, and the mean value of this power averaged over the first `2` seconds after the beginning of motion, `(m = 1,v = 2,r = 1)`.

A particle of mass `m` moves along a circle of radius `R` with a norma

1.	A particle of mass `m` moves along a circle of radius `R` with a normal acceleration varying with time as `a_(n) = bt^(2)`, where `b` is a constant. Find the time dependence of the power developed by all the forces acting on the particle, and the mean value of this power averaged over the first `2` seconds after the beginning of motion, `(m = 1,v = 2,r = 1)`.
Answer» Correct Answer - `2` `rArr v = sqrt(bR) t (dv)/(dt) = sqrt(bR)` For circular motion work done by normal force is zero. For tangential forces. `F_(t)=m(dv)/(dt)=m sqrt(bR) P=F_(t).v = F_(t) v cos theta` as `theta = 0^@`, `P = F_(t) v = mbRt` Average power `= (underset(0) overset(T) intP(t)dt)/(underset(0) overset(T)int dt) = underset(0) overset(T) int(mbRTdt)/(T)` =`(mbR(t^(2)//2)_(0)^(T))/(T) = (mbRt)/(2)`.

Discussion

No Comment Found

Related InterviewSolutions

A body is allowed to slide down a frictionless track from rest position at its top under gravity. The track ends in a circular loop of diameter `D`. Then, the minimum height of the inclined track (in terms of `D`) so that it may complete successfully the loop isA. `7D//4`B. `9D//4`C. `5D//4`D. `3D//4`
A body of mass `2 kg` is projected with an initial velocity of `5 ms^(-1)` along a rough horizontal table. The work done on the body by the frictional forces before it is brought to rest isA. 250 JB. 25 JC. `-250 J`D. `-25 J`
A particle is projected along a horizontal field whose coefficient of friction varies as `mu=A//r^2`, where r is the distance from the origin in meters and A is a positive constant. The initial distance of the particle is `1m` from the origin and its velocity is radially outwards. The minimum initial velocity at this point so the particle never stops isA. `infty`B. `2 sqrt(gA)`C. `sqrt(2 gA)`D. `4 sqrt(gA)`
A particle of mass `m` is projected at an angle `alpha` to the horizontal with an initial velocity `u`. The work done by gravity during the time it reaches its highest point isA. `u^(2) sin^(2) alpha`B. `(m u^(2) cos^(2) alpha)/(2)`C. `(m u^(2) sin^(2) alpha)/(2)`D. ` - (m u^(2) sin^(2) alpha)/(2)`
A car, moving with a speed of `50 km//hr`, can be stopped by brakes after at least `6 m`. If the same car is moving at a speed of `100 km//hr`, the minimum stopping distance isA. 6 mB. 2 mC. 18 mD. 24 m
A particle is projected at `t = 0` from a point on the ground with certain velocity at an angle with the horizontal. The power gravitational force is plotted against time. Which of the following is the best representation ?A. B. C. D.
A body is moved along a straight line by a machine delivering constant power . The distance moved by the body is time `t` is proptional toA. `t^(1//2)`B. `t^(3//4)`C. `t^(3//2)`D. `t^(1//4)`
A ball is thrown vertically upwards from the ground. Work done by air resistance during its time of flight isA. positive during ascent and negative during descentB. positive during ascent and descentC. negative during ascent and positive during descentD. negative during ascent and descent
A particle of mass `100 g` is thrown vertically upwards with a speed of `5 m//s`. The work done by the force of gravity during the time the particle goes up isA. `-0.5 J`B. `-1.25 J`C. `1.25 J`D. `0.5 J`
In the pulley-block system shown in figure, strings are light. Pulleys are massless and smooth. System is released from rest. In `0.3` seconds. . (a) work done on `2 kg` block by gravity is `6 J` (b) work done one `2 kg` block by string is `-2 J` ( c) work done on `1 kg` block by gravity is `-1.5 J` (d) work done on `1 kg` block string is `2 J`.A. only `a,d` are correctB. only `b,d` are correctC. only `a,b,c` are correctD. All are correct

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment