Question

The radius ofcircle, the period of revolution, initial position and sense of revolution are indicated in the fig.
y - projection of the radius vector of rotating particle P is :
(1) y(t) = –3 cos2πt, where y, in m
(2) y(t) = 4 sin(πt/2), where y in m
(3) y(t) = 3 cos(3πt/2), where y in m
(4) y(t) = 3 cos(πt/2), where y in m

Answer 1

y - projection of the radius vector of rotating particle P is $\bold{y=3Cos\frac{\pi t}{2}}$.

Step by step explanation:

• Displacement is the shortest between the initial position to the final position of the body.
• Displacement is a vector quantity.

From the given,

"y" displacement is maximum at "t = 0".

Time required for the displacement  = 4s

Displacement can be calculated by the following formula.

                       $\bold{\omega =\frac{2 \pi}{T}}$.......................(1)

Substitute the given values in equation (1)

                          $\Rightarrow \frac{2 \pi}{4}=\frac{\pi}{2}rad/s$

                               $y=acos\omega t$

                               $y=3cos \frac{\pi t}{2}$

Hence, correct option is 4.