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Chapter 5: Problem 582

An automobile engine develops \(100 \mathrm{kw}\) when rotating at a speed of 1800 r.p.m. what torque does it deliver? \(\\{\mathrm{A}\\} 350 \mathrm{Nm} \quad\\{\mathrm{B}\\} 440 \mathrm{Nm}\) \\{C \(\\} 531 \mathrm{Nm} \quad\\{\mathrm{D}\\} 628 \mathrm{Nm}\)

Short Answer

Expert verified
The short answer is: The torque delivered by the engine is approximately \(531\,\mathrm{Nm}\) (Option \(\mathrm{C}\)).

Step by step solution

01

Convert RPM to radians per second

Before we can use the given formula to calculate torque, we need to convert the rotational speed from RPM (revolutions per minute) to radians per second. First, we should know that there are 2π radians in one revolution. Also, 1 minute has 60 seconds. Therefore, to convert 1800 RPM to radians per second: \[Angular\,Speed (rad/s) = 1800\,RPM × \frac{2π\,rad}{1\,revolution} × \frac{1\,min}{60\,s}\]
02

Calculate Angular Speed

To find the angular speed in radians per second, plug the values in the conversion equation: \[Angular\,Speed (rad/s) = 1800 × \frac{2π}{1} × \frac{1}{60}\] \[Angular\,Speed (rad/s) = 1800 × \frac{π}{30}\] \[Angular\,Speed (rad/s) = 60π\,rad/s\]
03

Use the power-torque formula

Now, we will use the formula that relates power, torque, and angular speed to find the torque: \[Power = Torque × Angular\,Speed\] Next, we need to rearrange the formula to solve for torque: \[Torque = \frac{Power}{Angular\,Speed}\]
04

Calculate the torque

Now, we can calculate the torque by plugging in the given power and the calculated angular speed from Step 2: \[Torque = \frac{100\,\mathrm{kW}}{60π\,\mathrm{(rad/s)}}\] We first need to convert power from kilowatts (kW) to watts (W) by multiplying by 1000: \[Torque = \frac{100,000\,\mathrm{W}}{60π\,\mathrm{(rad/s)}}\] Now divide the power by angular speed: \[Torque ≈ \frac{100,000}{188.496}\] \[Torque ≈ 530.518\,\mathrm{Nm}\]
05

Choose the correct option

Since the calculated torque is approximately 530.518 Nm, the closest answer to this value is \(\mathrm{C:}\) 531 Nm. So the correct option is \(\mathrm{C:}\) 531 Nm.

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Most popular questions from this chapter

A car is moving at a speed of \(72 \mathrm{~km} / \mathrm{hr}\) the radius of its wheel is \(0.25 \mathrm{~m}\). If the wheels are stopped in 20 rotations after applying breaks then angular retardation produced by the breaks is \(\ldots .\) \(\\{\mathrm{A}\\}-25.5 \mathrm{rad} / \mathrm{s}^{2}\) \(\\{\mathrm{B}\\}-29.52 \mathrm{rad} / \mathrm{s}^{2}\) \(\\{\mathrm{C}\\}-33.52 \mathrm{rad} / \mathrm{s}^{2}\) \(\\{\mathrm{D}\\}-45.52 \mathrm{rad} / \mathrm{s}^{2}\)

If the earth is treated as a sphere of radius \(R\) and mass \(M\). Its angular momentum about the axis of rotation with period \(\mathrm{T}\) is..... \(\\{\mathrm{A}\\}\left(\pi \mathrm{MR}^{3} / \mathrm{T}\right)\) \(\\{\mathrm{B}\\}\left(\operatorname{MR}^{2} \pi / \mathrm{T}\right)\) \(\\{C\\}\left(2 \pi \mathrm{MR}^{2} / 5 \mathrm{~T}\right)\) \(\\{\mathrm{D}\\}\left(4 \pi \mathrm{MR}^{2} / 5 \mathrm{~T}\right)\)

A player caught a cricket ball of mass \(150 \mathrm{gm}\) moving at a rate of \(20 \mathrm{~m} / \mathrm{s}\) If the catching process is Completed in \(0.1\) sec the force of the flow exerted by the ball on the hand of the player ..... N \(\\{\mathrm{A}\\} 3\) \(\\{B\\} 30\) \(\\{\mathrm{C}\\} 150\) \(\\{\mathrm{D}\\} 300\)

Statement \(-1\) - Two cylinder one hollow and other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow will reach the bottom of inclined plane first. Statement \(-2-\mathrm{By}\) the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline. \(\\{\mathrm{A}\\}\) Statement \(-1\) is correct (true), Statement \(-2\) is true and Statement- 2 is correct explanation for Statement \(-1\) \\{B \\} Statement \(-1\) is true, statement \(-2\) is true but statement- 2 is not the correct explanation four statement \(-1\). \\{C\\} Statement - 1 is true, statement- 2 is false \\{D \(\\}\) Statement- 2 is false, statement \(-2\) is true

Match list I with list II and select the correct answer $$ \begin{aligned} &\begin{array}{|l|l|} \hline \text { List-I } & \begin{array}{l} \text { List - II } \\ \text { System } \end{array} & \text { Moment of inertia } \\ \hline \text { (x) A ring about it axis } & \text { (1) }\left(\mathrm{MR}^{2} / 2\right) \\ \hline \text { (y) A uniform circular disc about it axis } & \text { (2) }(2 / 5) \mathrm{MR}^{2} \\ \hline \text { (z) A solid sphere about any diameter } & \text { (3) }(7 / 5) \mathrm{MR}^{2} \\ \hline \text { (w) A solid sphere about any tangent } & \text { (4) } \mathrm{MR}^{2} \\ \cline { 2 } & \text { (5) }(9 / 5) \mathrm{MR}^{2} \\ \hline \end{array}\\\ &\text { Select correct option }\\\ &\begin{array}{|l|l|l|l|l|} \hline \text { Option? } & \mathrm{X} & \mathrm{Y} & \mathrm{Z} & \mathrm{W} \\\ \hline\\{\mathrm{A}\\} & 2 & 1 & 3 & 4 \\ \hline\\{\mathrm{B}\\} & 4 & 3 & 2 & 5 \\ \hline\\{\mathrm{C}\\} & 1 & 5 & 4 & 3 \\ \hline\\{\mathrm{D}\\} & 4 & 1 & 2 & 3 \\ \hline \end{array} \end{aligned} $$
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