Question

A toy car is tied to the end of an unstretched string of a length, $a$. When revolved, the toy car moves in a horizontal circle of radius $2a$ with time period, $T$. If it is now revolved in a horizontal circle of radius $3a$ with a period $T^{\prime }$ with the same force, then

• A. $T^{\prime }=\frac{\sqrt{3}}{2}T$
• B. $T^{\prime }=\sqrt{\frac{3}{2}}T$
• C. $T^{\prime }=T$
• D. $T^{\prime }=\frac{3}{2}T$

Answer 1

Answer: (B)

$T^{\prime }=\sqrt{\frac{3}{2}}T$

$m\left(2a\right){\left(\frac{2\pi }{T}\right)}^2=m\left(3a\right){\left(\frac{2\pi }{T^{\prime }}\right)}^2$.

So, $\frac{T^{\prime }}{T}=\sqrt{\frac{3}{2}}$