Question

A machine requires a torque of $(300+50\sin 2\theta )$ to drive it. It is directly coupled to an engine producing a torque of $(300+50\sin \theta )$ in a cycle. How many times the value of torque of the machine and the engine will be the same?

• A. 1
• B. 2
• C. 4
• D. 8

Answer 1

The correct option is C 4

Here the cycle consists of ${360}^{\circ }$ because after that $T-\theta$ diagram will repeat.

$300+50\sin 2\theta =300+50\sin \theta$

$sin2\theta =\sin \theta$

General solution of this equation is

$2\theta =(2n-1)\pi -\theta ,2n\pi +\theta$

For $n=1,2\theta =\pi -\theta$

and $2\theta =2\pi +\theta$

$\Rightarrow \theta =\frac{\pi }{3},\theta =2\pi$

$Forn=2,2\theta =3\pi -\theta \Rightarrow \theta =\pi$

$Forn=3,2\theta =5\pi -\theta \Rightarrow \theta =\frac{5\pi }{3}$

$\therefore$Number of times are 4