| Aircraft Type | Description |
| I. Dornier-228 | Maritime patrol aircraft |
| II. IL-76 | Supersonic combat aircraft |
| III. C-17 Globemaster III | Military transport aircraft |
The question asks to identify the correctly matched pairs of aircraft types and their descriptions related to India's defence. We need to evaluate each pair individually based on our knowledge of military aircraft.
Based on the above analysis, pairs I and III are correctly matched, while pair II is incorrectly matched.
Correct Option: B) Only two
The question asks to identify the true statements about work. We will analyze each statement individually based on the fundamental definitions and theorems of work and energy in physics.
The question asks for the definition of a specific physical quantity. We need to recall the definitions of the options provided and identify which one matches "the rate of doing work".
where \(P\) is power, \(W\) is work done, and \(t\) is the time taken.
B) Power is defined as the rate at which work is done. It measures how quickly work is performed or energy is transferred. Its SI unit is the Watt (W), which is equivalent to one joule per second (J/s).
To determine which physical quantities have the dimension \(ML^2T^{-2}\), we need to recall the definitions and formulas for mechanical energy, kinetic energy, and potential energy, and then derive their dimensional formulas. All forms of energy have the same dimensions.
Understand the dimensions: The given dimension is \(ML^2T^{-2}\), where \(M\) represents Mass, \(L\) represents Length, and \(T\) represents Time.
Analyze Mechanical Energy: Mechanical energy is the sum of kinetic energy and potential energy. Since all forms of energy are interconvertible and represent the capacity to do work, they must have the same dimensions as work.
Analyze Kinetic Energy: Kinetic energy \((KE)\) is the energy possessed by an object due to its motion. It is given by the formula \(KE = \frac{1}{2}mv^2\), where \(m\) is mass and \(v\) is velocity.
Analyze Potential Energy: Potential energy \((PE)\) is the energy stored in an object due to its position or state. For gravitational potential energy, it is given by the formula \(PE = mgh\), where \(m\) is mass, \(g\) is acceleration due to gravity, and \(h\) is height.
Conclusion: All three quantities (Mechanical energy, Kinetic energy, and Potential energy) have the dimension \(ML^2T^{-2}\).
Correct Option: D) All the above
The problem asks us to calculate the power utilized given the work done and the time taken. Power is defined as the rate at which work is done or energy is transferred. The formula for power is Work divided by Time.
Power \((P)\) is defined as the work done per unit time.
\[ P = \frac{W}{t} \]Substitute \(W = 1000 \text{ J}\) and \(t = 2 \text{ s}\) into the power formula:
\[ P = \frac{1000 \text{ J}}{2 \text{ s}} \]Perform the division:
\[ P = 500 \text{ J/s} \]The unit J/s (Joules per second) is equivalent to Watts (W).
\[ P = 500 \text{ W} \]C) 500 W is the correct answer. The power utilized is 500 Watts, as calculated by dividing the work done (1000 J) by the time taken (2 s).