Question

A spring balance hanging in steady state inside a train moving on a straight track shows a reading of double the actual mass of an object. Calculate the acceleration of the train.

• A. $\sqrt{5}g$
• B. $\sqrt{2}g$
• C. $\sqrt{6}g$
• D. $\sqrt{3}g$

Answer 1

The correct option is D $\sqrt{3}g$

FBD of object from accelerating frame assuming that train is moving rightward with the acceleration $a$ and block will experience a pseudo force in leftward as shown in the figure.
$F_{pseudo}=ma$


At equilibrium, $F_{net}=Kx$
$\Rightarrow Kx=\sqrt{(mg{)}^2+(ma{)}^2}$
$\Rightarrow F_{spring}=m\sqrt{g^2+a^2}$
According to question,
$F_{spring}=2mg$
$\Rightarrow m\sqrt{g^2+a^2}=2mg$
$\Rightarrow \sqrt{g^2+a^2}=2g$
$\Rightarrow g^2+a^2=4g^2$
$\Rightarrow a=\sqrt{3g^2}=\sqrt{3}g$