MCQ : Work And Energy - 2 - UPSC MCQ

When the speed of a body is tripled, the change in kinetic energy (K.E.) can be calculated as follows:

 

• The work done by the moon when it revolves around the earth is zero because here displacement of the moon and gravitational force of earth are perpendicular to each other.
• Work done (W) = F x d x cosƟ. In the case of the revolution of the moon around the earth, Ɵ is 90°. Thus, W = F x d x cos90° = F x d x 0 = 0.
• So, the work done by the moon when it revolves around the earth is Zero.

Work done = Mgh
Work will be maximum when the change in height is maximum, thus when it is lifted vertically upward.

Potential energy is mathematically defined as, P.E = mgh
Potential energy of body 1 = P.E₁ = mgh₁ 
Potential energy of body 2 = P.E₂ = mgh₂ 
Since weight of two bodies are equal, therefore, P.E₁ / P. E₂ =  h / 1.5 h = 2:3 

Given: Velocity = v & Force = F
We know that work done is equal to the product of force and displacement.
W = F*d
Dividing by t on both sides then we get:
W/t = F*d/t
d/t = v ( Speed = Distance/ Time)
W/t = P (Power)
Therefore, P = F*v

Potential energy is energy stored in matter. Joule is the SI unit of energy.

• Energy at start will be = Potential Energy = mgh
• According to the law of conservation of energy, it's total energy will be the same at all points i.e. = mgh.

Work = Force * Displacement (N-m)

• Two bulbs of 40 W and 60 W are connected in series to an external potential difference. 
•  When two bulbs are connected in series, the current I will be the same. But the resistance varies. Higher the resistance brighter the glowing. 
• P = V² / R
  ⇒ P, R are inversely proportional to each other. 
  Hence, P₄₀ < P₆₀
  ⇒ R₄₀ > R₆₀
• So, the resistance of 40 W bulb is higher than the 60 W bulb. So 40 W bulb will dissipate more power and glow brighter.

Force and displacement are in the same direction. 
So, the work done is positive.

Explanation:
When a boy holds a mass on his stretched hand, several factors come into play. Let's analyze the options given to determine the correct answer:
A: Work done against gravity is zero.
- This statement is not true because the boy is holding the mass against the force of gravity. Work is being done against gravity to keep the mass elevated, so the work done against gravity is not zero.
B: Muscular energy is used.
- This statement is true. To hold the mass on his stretched hand, the boy needs to exert force using his muscles. This requires the use of muscular energy.
C: Both (a) and (b)
- This option is the correct answer. Both statements (a) and (b) are true. Work is being done against gravity, and muscular energy is used to hold the mass.
D: Neither (a) nor (b)
- This option is incorrect because both statements (a) and (b) are true.
In conclusion, when a boy holds a mass on his stretched hand, work is done against gravity, and muscular energy is used. Therefore, the correct answer is option C: Both (a) and (b).

They will have the same acceleration due to gravity because it is independent of mass. 

• Since the free-falling acceleration is not dependent on mass, the final velocities of both masses are the same.
  The kinetic energy = KE = mv²/2
• Hence, the kinetic energy of the heavier mass will be more.

• Work done by any force is the product of the component of the force in the direction of displacement and the magnitude of displacement.
  W = F.d = Fd cosθ
• When  W =−ve, it means cosθ = −ve
  Therefore, θ = 180º

• In the given question, P is given in Watt and we have to calculate E in kWh. So,  we have to convert watt into kW. For this, we divide Pt by 1000.
• Therefore, E = Pt / 1000  is the correct answer.