Test: Energy & Power - JEE MCQ

We know that power (P) = force (F) x velocity (v).

Since the body is moving with acceleration,v changes and as a result of that P also changes,F being constant.

For P to be constant, F v = constant or F ∝ 1/v i.e 

Force should be inversely proportional to the velocity of the body.

Thus,as v increases, F should decrease to keep P constant. 

Power = work done / time 
work = force x distance 
so power = (force x distance) / time 
time = (force x distance) / power 
= (2000 N x 40m) / 10000W = 8 seconds

For person A,
Mass of body, m₁ = 5kg
Coefficient of friction, μ =0.3
So, The force of friction,
F1= μm₁g=0.3 X 5 X 10=15N
Displacement, S₁=4m
Therefore,
Work done, W₁=15X4=60J
Time taken, t₁=15sec
So, Power, P₁=60/15=4W
For Person B
Mass of body, m₂=7kg
Coefficient of friction, μ =0.3
So, The force of friction,
F₁= μm₂g=0.3 X 7 X 10=21N
Displacement, S2=3m
Therefore,
Work done, W₂=21X3=63J
Time taken, t₂=15sec
So, Power, P₃=63/15=4.2W

So person B has more energy and power.

P = p Cos(t) i + p Sin(t) j

dP/dt = -p Sin(t) j + p Cos(t) i

Work done, W = P²/2m

Rate of work done = d/dt(P²/2m)

= 2P/²m x dP/dt

= P/m x dP/dt

= -p².Sin(t).Cos(t) + p².Sin(t).Cos(t)

=> Rate of work done = 0

According to question, 60 kg man runs up a staircase in 12 sec.

m₁ = 80 kg

t₁ = 12 sec

=> A 50 kg man runs up the same staircase in 11 sec:

m₂ = 60 kg

t₂ = 11 sec

=> Rate of work done is equals to power.

∴ P = E/ t and E = mgh

∴ P₁ = m₁gh / t₁

P₂ = m₂gh/ t₂

=> The ratio of Power or Rate of work done is:

P₁/P₂ = m₁gh / t₁ / m₂gh/ t₂

= m₁ * t₂ / m₂ * t₁

= 80x11/60x12

= 11 : 9

Thus, the ratio of rate of doing their work is 11 : 9.

As the momentum, P = mv is doubled, we get the new velocity is 2v as mass can’t be increased. Thus if initial KE = ½ mv²
We get new KE = ½ m (2v)2
= 4 times the original one.

F=4500N
v=2ms⁻¹
The power of motor is given by
P=F.v
P=4500×2
P=9000W=9kW

Power = work done / time taken

or P = mgh / t

P = (m/t) gh = 100 x 10 x 100 = 100 kW

Power =F.V 
i.e, Power = force x velocity.
here, force (f)= 10N
and velocity (v) = 3.65 m/s
so, Power = f x v,
i.e, 10 x 3.65 = 36.5 w.

We know that P = F.v
= m.a.a.t
And with u= 0 we have s = ½ at²
Thus we get s = ½ 
Thus as P is constant and m is always the same 
we get s is function of t^3/2