Question

A particle is moving on a straight line with a speed of about 0.5 m/s. To measure its speed, points are marked on the line of motion, which are exactly separated by 5 mm. To have an accuracy of 99% in the determination of speed, the minimum least count of the measuring clock is n x 10-4 s. Find value of n ​

Answer 1

Given:- speed= 0.5m/s

accuracy= 99%

d= 5mm

To find:- least count of clock

Solution:-

According to the given data, we can say that

V=0.5m/s d=5mm = 5*10^-3 m

Now find the time required for this motion,

v = d / t

t = d/V

t = 5*10^-3 / 0.5

t = 10*10^-3

therefore the time calculated is 0.01s

Now the given accuracy is 99%

use the below formula,

Δt/t = 99/100

Δt = 99 * 10^-2 *10^-2

Δt = 99 * 10^-4

Δt = 0.0099s

The value of least count is 99 * 10^-4.

Hence the value of n is 99.