Question

A smooth table is placed horizontally and an ideal spring of spring constant $k = 1000\mspace{6mu} N/m$ and unextended length of $0.5m$ has one end fixed to its centre. The other end is attached to a mass of $5kg$ which is moving in a circle with constant speed $20m/s$. Then the tension in the spring and the extension of this spring beyond its normal length are

• A. $500\mspace{6mu} N,\mspace{6mu} 0.5\mspace{6mu} m$
• B. $600\mspace{6mu} N,\mspace{6mu} 0.6\mspace{6mu} m$
• C. $700\mspace{6mu} N,\mspace{6mu} 0.7\mspace{6mu} m$
• D. $800\mspace{6mu} N,\mspace{6mu} 0.8\mspace{6mu} m$

Answer 1

Answer: (A)

$500\mspace{6mu} N,\mspace{6mu} 0.5\mspace{6mu} m$

Answer 2

$k = 1000,m = 5kg,l = 0.5m,v = 20m/s$ (given)

Restoring force = kx $= \frac{mv^{2}}{r} = \frac{mv^{2}}{l + x}$ ⇒ $1000x = \frac{5(20)^{2}}{0.5 + x}$ ⇒ $x = 0.5m$

and Tension in the spring = kx $= 1000 \times \frac{1}{2} = 500N$