hkale 2003

We actually can ignore the horizontal movement of the particle since it is moving with constant horizontal speed, and this cannot help us determine the frequency of the stroboscope.

So, we consider the vertical motion.

Let downward direction be positive. And let u be the initial downward speed of the particle. Let t be the time interval of the stroboscope.

Consider the first one, downward displacement, s1 = 15 cm = 0.15 m

By s1 = ut + 1/2 gt2

0.15 = ut + 1/2 (10)t2

0.15 = ut + 5t2 ... (1)

Now, consider the particle has moved two strobes.

Downward displacement, s2 = 40 cm = 0.4 m

By s2 = u(2t) + 1/2 g(2t)2

0.4 = 2ut + 20t2 ... (2)

(2) - 2 X (1):

0.1 = 10t2

Time interval, t = 0.1 s

Frequency, f = 1 / t = 1 / 0.1 = 10 Hz

So, the answer is C.