Question

Two rubber threads of spring constant 100 N/m each is connected to the two sides of a body of mass 1 kg standing on a horizontal frictionless surface.The rubber threads are stretched by a length of $\Delta l=1cm$ and their ends are fixed. Then the body is displaced by a distance of $2\Delta l$ towards one of the fixing points and it is released.Find the initial acceleration of the mass:

• A. $1m/s^2$
• B. $2m/s^2$
• C. $3m/s^2$
• D. None of these

Answer 1

The correct option is C $3m/s^2$

By Hook's law

$F=-k\times x=m\times a$
here $x=3cm$ (1cm of initial stretch and 2cm of later displacement, because one of the elastic become totally loose when it displaced towards one fixed end that causes all the initial force on the mass will be only due to the elastic on the other side)
$F=-100\times 3\times {10}^{-2}Kg\times \frac{m}{se{c}^2}=1Kg\times a$
$a=3m/se{c}^2$