question_answer

A spot of light S rotates in a horizontal plane with a constant angular velocity of 0.1 rad/s. The spot of light P moves along the wall at a distance of 3 m from S. The velocity of spot P, where\[\theta =45{}^\circ ,\]is

A)  0.5 m/s               

B)  0.6 m/s

C)  0.7 m/s               

D)  0.8 m/s

Correct Answer: B

Solution :

                 The situation is shown in figure. From figure, \[x=r\text{ }\tan \theta \] \[\therefore \]Velocity of P is \[v=\frac{dx}{dt}=r{{\sec }^{2}}\theta \left( \frac{d\theta }{dt} \right)\] where, \[\frac{d\theta }{dt}\]angular velocity of rotation of spot                 \[=\omega \] \[\therefore \]  \[v=\omega r{{\sec }^{2}}\theta \] At\[\phi =45{}^\circ ,\]so\[\theta =45{}^\circ \] Hence,  \[v=0.1\times 3\times {{\sec }^{2}}{{45}^{o}}\] \[=0.1\times 3\times 2=0.6\text{ }m/s\]