Physics - NLM Question with Solution | TestHub

Let the acceleration of the system be $a$. Since $M<6\text{ kg}$, the $6\text{ kg}$ mass moves downwards and mass $M$ moves upwards.

For the $6\text{ kg}$ mass, the equation of motion is:
$6g-T=6a$

Given $T=45\text{ N}$ and $g=10{\text{ m/s}}^2$:
$6(10)-45=6a$
$60-45=6a$
$15=6a\Rightarrow a=2.5{\text{ m/s}}^2$

For the mass $M$, the equation of motion is:
$T-Mg=Ma$

Substituting the values of $T$, $g$, and $a$:
$45-M(10)=M(2.5)$
$45=10M+2.5M$
$45=12.5M$
$M=\frac{45}{12.5}=3.6\text{ kg}$

Answer: $3.6\text{ kg}$