Question

A spring balance whose maximum extension of its spring is 20 cm can sustain a maximum load of $20k{g}_{wt}$ within its elastic limit on the surface of the earth. Now the same balance is taken to the moon. Given that $g_{earth}=6g_{moon},$ what is the maximum mass of the load that can be attached to the balance to have half its maximum extension?

• A. $76$
• B. $65$
• C. $60$
• D. $55$

Answer 1

The correct option is C $60$

(i) Find the maximum load (i.e), $20k{g}_{wt}$ in terms of newtons?
Convert 20 cm length in terms of S.I.
Find the value of force constant (k) from the formula, $F=kx$......(1)
Now, find the maximum load that is possible on the surface of the moon if $F=m{g}_m=kx$ ($g_
{m}$ acceleration due to gravity on the moon).
Substitute the value of $\frac{g_E}{6}$ for $g_m$.---------(2)
Now, find the mass of the load that is attached to have its maximum extension ------(3)
Divide the value obtained in (3) by (2).
Then this gives maximum mass of the load that can be attached to the balance to have half its
maximum extension.
(ii) 60 kg