20 Questions MCQ Test Science & Technology for UPSC CSE - MCQ : Work And Energy - 2
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A: 50 kg man climbing a ‘slant length of 5 m along a 30° incline.
B: 25 kg man running with 2 m/s speed.
C: A force of 5 N acting on an object moving with 5 m/s speed for 5 min.
If the energies in A, B and C are EA, EB and EC respectively, then:
Detailed Solution for MCQ : Work And Energy - 2 - Question 5
Ea = mv2/2 = 50 x 10 x 5sin30º = 250j
Eb = mv2/2 = 25 x 4/2 = 50j
Ec = fvt = 5 x 25 x 60 = 7500j
Therefore, Eb < Ea < Ec
Two bodies of equal weight are kept at heights of h and 1.5 h, respectively. The ratio of their potential energies is:
Detailed Solution for MCQ : Work And Energy - 2 - Question 6
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
If a force of F newton moves a body with constant speed v, the power delivered by it is:
Detailed Solution for MCQ : Work And Energy - 2 - Question 7
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
Detailed Solution for MCQ : Work And Energy - 2 - Question 13
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).
Detailed Solution for MCQ : Work And Energy - 2 - Question 17
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.
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.
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.
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