Question

It takes 10 min to cover a round of a circular rope at speed 10cm/s. If the rope is kept as a straight line, the constant acceleration needed to complete the path in 5 min is.

• A. $\frac{1}{1500}$ $m{s}^{-2}$
• B. $\frac{1}{1000}$ $m{s}^{-2}$
• C. $\frac{1}{500}$ $m{s}^{-2}$
• D. $\frac{1}{750}$ $m{s}^{-2}$

Answer 1

The correct option is D $\frac{1}{750}$ $m{s}^{-2}$

Given, speed $=10cm{s}^{-1}$ = $\frac{10}{100}$ $=0.1m{s}^{-1}$ and time taken = 10 minutes $=10\times 60=600s$
Length of the rope = speed $\times$ time = 0.1 $\times$ 600 = 60 m
Now we have to cover distance 60 m in half the time, i.e. 5 minutes
Using second equation of motion, $s=ut+\frac{1}{2}a{t}^2$
$60=0+\frac{1}{2}\times a\times (60\times 5{)}^2$
On solving we get, $a=\frac{1}{750}$ $m{s}^{-2}$