Answer

Verified

47.1k+ views

**Hint:**In the given question, we are given with the angular velocity of the motor engine and the time for which it works. We can also see that there will be angular declaration, which is given as constant in the problem. Now, to find the number of revolutions we will use the relation between all these properties.

**Formula used:**We will use formula for angular displacement $\theta = {\omega _0}t + \dfrac{1}{2}\alpha {t^2}$ and angular acceleration $\omega = {\omega _0} + \alpha t$

**Complete step by step answer:**

In the above question, we are given that

Initial angular velocity is $100\dfrac{{rev}}{m}$

Now, converting angular velocity to rad/sec,

$rad/s = \dfrac{{rev/m}}{{60\sec /m}} \times 2\pi rad/rev$

Now, substituting the value,

$

\Rightarrow \dfrac{{100}}{{60}} \times 2\pi rad/\sec \\

\Rightarrow \dfrac{{10}}{3}\pi rad/\sec \\

$

Hence, the initial angular velocity in rad/sec is $\dfrac{{10}}{3}\pi rad/\sec $

Total time interval is $15s$ .

Now, we will use formula for angular acceleration,

That is $\omega = {\omega _0} + \alpha t$, where $\omega $ is the final velocity, ${\omega _0}$ is the initial velocity, $\alpha $ is the angular acceleration and $t$ is the time interval.

Now, substituting the values given in the problem,

\[

\omega = {\omega _0} + \alpha t \\

\Rightarrow 0 = \dfrac{{10}}{3}\pi + \alpha 15 \\

\Rightarrow \alpha = - \dfrac{2}{9}\pi \\

\]

Now, the angular acceleration is $ - \dfrac{2}{9}\pi rad/{s^2}$

Now, using the formula for angular displacement $\theta = {\omega _0}t + \dfrac{1}{2}\alpha {t^2}$

$

\Rightarrow \theta = {\omega _0}t + \dfrac{1}{2}\alpha {t^2} \\

\Rightarrow \theta = \dfrac{{10}}{3}\pi \left( {15} \right) - \dfrac{1}{2} \cdot \dfrac{2}{9}\pi {\left( {15} \right)^2} \\

\Rightarrow \theta = \pi \left( {15} \right)\left( {\dfrac{{30 - 15}}{9}} \right) \\

\Rightarrow \theta = 25\pi rad = 12.5rev \\

$

**Hence, the answer for the above problem is $12.5$ revolutions.**

**Note:**In the given question, we know that when the engine is switched off the final velocity will be zero, as the motor goes to rest. We also know that the angular acceleration will be also negative as the body is decelerating. Now, we will use the certain formulas to find the number of revolutions made by the motor before coming to rest.

Recently Updated Pages

To get a maximum current in an external resistance class 1 physics JEE_Main

f a body travels with constant acceleration which of class 1 physics JEE_Main

A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main

If the beams of electrons and protons move parallel class 1 physics JEE_Main

Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main

silver wire has diameter 04mm and resistivity 16 times class 12 physics JEE_Main

Other Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

The nitride ion in lithium nitride is composed of A class 11 chemistry JEE_Main

An electric dipole is placed in an electric field generated class 12 physics JEE_Main

Explain the construction and working of a GeigerMuller class 12 physics JEE_Main