MCQ : Work And Energy - 2 - UPSC

K.E. ∝ v²
So when v → 3v, K.E. → 9K.E.

• 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.

Cost of Electricity = P*t*cost per kW
=0.06 kW x (5 x 30) x 3= Rs. 27

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

E_a = mv²/2 = 50 x 10 x 5sin30º = 250j
E_b = mv²/2 = 25 x 4/2 = 50j
E_c  = fvt = 5 x 25 x 60 = 7500j
Therefore, E_b < E_a < E_c​

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.

Power = P = Energy/Time​ = Work/Time
P_A​= 500/10*60 ​= 0.83J/s
P_B= 600/20*60 ​= 0.5J/s
P_A > P_B

 

Momentum Conservation in Collisions

In a collision, the momentum of the system is conserved. This means that the total momentum before the collision is equal to the total momentum after the collision, regardless of the type of collision.

Explanation:

When two objects collide, they exert forces on each other for a short period of time. These forces cause changes in the objects' velocities, resulting in a transfer of momentum between them. However, the total momentum of the system (the two objects combined) remains constant.

Here's a more detailed explanation of why momentum is conserved in collisions:

1. Law of Conservation of Momentum:

The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In a collision, the system may not be isolated due to external forces such as friction or air resistance. However, if these external forces are negligible or canceled out, the conservation of momentum still holds true.

2. Impulse-Momentum Principle:

The impulse-momentum principle states that the change in momentum of an object is equal to the impulse applied to it. Impulse is defined as the product of force and the time interval over which it acts. In a collision, the forces exerted by the objects on each other result in impulses that cause changes in their momentum.

3. Types of Collisions:

There are three main types of collisions:

• Elastic Collision: In an elastic collision, both momentum and kinetic energy are conserved. This means that after the collision, the objects bounce off each other without any deformation or loss of energy.


• Inelastic Collision: In an inelastic collision, momentum is conserved, but kinetic energy is not. The objects may stick together or deform during the collision, resulting in a loss of kinetic energy.


• Perfectly Inelastic Collision: In a perfectly inelastic collision, the objects stick together and move as one mass after the collision. Momentum is conserved, but kinetic energy is lost.

Conclusion:

In summary, in a collision, the momentum of the system is always conserved. The type of collision determines whether kinetic energy is conserved or lost. The conservation of momentum is a fundamental principle in physics and is applicable to various real-world scenarios, including car crashes, billiard ball collisions, and 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.

• Work done by any force is the product of the force in the direction of displacement and the magnitude of displacement. The work done depends upon the force and displacement.
• W = F.d, when force and displacement are perpendicular to each other work done is zero.
• Hence work done also depends upon the angle between Force and Displacement but not on the velocity of the moving object.