Test: Work & Energy - JEE MCQ

Hence, the Correct Answer is option A

Given, Kinetic energy increases uniformly with time
K.E ∝ t
Kinetic energy can be written as KE= ½ mv² so we can write
½ mv² ∝ t

Therefore, v ∝ √t
According to Newton's second law, force (F) is inversely proportional to velocity (F ∝ 1/v). 
F ∝ 1/v
Therefore,
F ∝ 1/√t

Hence, Correct Answer is Option B

We know that Work done, W = F.s
where F is force and s is displacement due to that force.
Thus rate of work done is: 

dW/dt = d(F.s)/dt

So as F is constant we get, 
dW/dt = F.d(s)/dt = F.v = P (Power)

X and Y have equal kinetic energy but their masses are m and 4m respectively.
► 1/2 m₁v₁² = 1/2 m₂v₂²  
► mv₁² = 4m * v₂²  
► v₁ : v₂ = 2 : 1
Hence the ratio of their linear momentum is:
m1v1 : m2v2 = m * 2v : 4m * v = 1 : 2

m = 5 kg,
h = 3 m,
g = 9.81 m/s^-2

We know that,
Potential energy = mgh

= 5 * 9.81 * 3 = 147.15 J

Hence, the correct answer is Option C.

► η = work output / heat input​
► η = 50% = 50/100 = 1/2
► 1/2 = 4500 / Heat input
► Heat input = 9000 J

The kinetic energy is given by: 

KE= p²/2m

So, ΔKE = 2pΔp​ / 2m = pΔp / m​
ΔKE / KE ​= (pΔp/m)​ * (2m/p²)​ = 2Δp / p
Since the momentum p increases by 20%, so the final momentum becomes 1.2p.
Hence, KE_final​ = (1.2p)² / 2m​ = 1.44p² / 2m​ = 1.44KE
So, % change in KE = 44%

• If a force acting on a body has a component in the opposite direction of displacement, the work done is negative.
• So when a body slides against a rough horizontal surface, its displacement is opposite to that of the force of friction. The work done by the friction is negative.

Each bullet will have KE = 1/2 * 0.05 * 700 * 700 = 12250 J
So for 60 bullets the energy given by machine in 60 second = 60 x 12250 J
Hence power developed = Energy / time =60 x12250/60 =12250W
Or power = 12.250 kW.

If a force acts perpendicular to the direction of a body, the amount of work done is zero because there is no displacement in the direction of a force.