In electric power, if a body makes N rpm and the torque acting is T newton-meter, then work done per minute wi

Question

In electric power, if a body makes N rpm and the torque acting is T newton-meter, then work done per minute will be ______.

Examoogle · Accepted Answer

The correct answer is Option D: 2\pi NT 	ext{ joules}. Work done is defined as the product of torque and angular displacement. For a rotating body completing $N$ revolutions per minute, the total angular displacement in one minute is $2\pi N$ radians, resulting in a total work done of $2\pi NT$ Joules.

Step-by-Step Solution & Concepts:
Work done is defined as the product of torque and angular displacement. For a rotating body completing $N$ revolutions per minute, the total angular displacement in one minute is $2\pi N$ radians, resulting in a total work done of $2\pi NT$ Joules.

Working Principle: In rotational mechanics, work $W$ is equivalent to torque $T$ multiplied by the angular displacement $	heta$. Since one revolution corresponds to $2\pi$ radians, $N$ revolutions per minute corresponds to $2\pi N$ radians per minute. Therefore, $W = T 	imes (2\pi N)$.

Key Formulas: $W = T 	imes 	heta$ — general work-torque relation; $W = T 	imes (2\pi N)$ — work done per minute in joules; $P = \frac{2\pi NT}{60}$ — power in watts

Key Points: Torque is the rotational equivalent of force; Angular displacement for one revolution is $2\pi$ radians; Power is the rate of doing work, calculated by dividing the work done per minute by 60 seconds; The unit of work is Joules (J)

Advantages: Direct derivation from rotational kinematics; Fundamental definition applicable to all electrical machines

Applications: Calculation of energy output of electric motors; Design of rotating machinery in power systems

Additional Info: The expression $\frac{2\pi NT}{60}$ represents the power in Watts, not the work done per minute.. Option C refers to Power, while Option D refers to Work Done per minute.

Answer: D is correct — The total work done per minute is the product of the total angular displacement in radians ($2\pi N$) and the torque ($T$).

Exam Tip: Always distinguish between Work Done ($T 	imes 	heta$) and Power ($Work / Time$). Work done per minute is simply $T 	imes 2\pi N$, whereas Power is $T 	imes \omega$.

Examoogle · Answer

Option A: mgh joules

Examoogle · Answer

Option B: m 	imes g joules

Examoogle · Answer

Option C: \frac{2\pi NT}{60} 	ext{ joules}

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)