A) 350.67 N
B) 540.11 N
C) 311.64 N
D) 300.5 N
Correct Answer: C
Solution :
[c] : The 30 cm length of the scale reads up to 60 kg. \[\therefore \]Maximum force, \[F=60\text{ }kg\text{ }wt=60\times 9.8\text{ }N\] \[=588N\]and maximum extension, \[x=30-0=30\text{ }cm\]\[=30\times {{10}^{^{-2}}}m\] Spring constant of the spring balance is \[k=\frac{F}{x}=\frac{588N}{30\times {{10}^{-2}}m}=1960N/m\] Let a body of mass m is suspended from this balance. Then, time period of oscillation, \[T=2\pi \sqrt{\frac{m}{k}}\]or\[{{T}^{2}}=\frac{4{{\pi }^{2}}m}{k}\] \[\therefore \]\[m=\frac{{{T}^{2}}k}{4{{\pi }^{2}}}=\frac{{{(0.8)}^{2}}\times (1960)}{4\times {{(3.14)}^{2}}}=31.8kg\] Weight of the body \[=mg=(31.8\text{ }kg)(9.8\text{ }m/{{s}^{2}})\] \[=311.64N\]
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