Question

if a force$10\hat{i}+15\hat{j}+25\hat{K}$ acts on a system and gives an acceleration $2\hat{i}+3\hat{j}-5\hat{K}$ to the centre of mass of the system, the mass of the system is :

• A. 5 units
• B. $\sqrt{38}units$
• C. $5\sqrt{38}units$
• D. None

Answer 1

Answer: (A)

5 units

Given,

$F_{cm}=10\hat{i}+15\hat{j}+25\hat{k}{a}_{cm}=2\hat{i}+3\hat{j}-5\hat{k}$

We know that force is multiplication of mass and acceleration therefore,

$F_{cm}=m\hat{a}10\hat{i}+15\hat{j}+25\hat{k}=m(2\hat{i}+3\hat{j}-5\hat{k})m=\frac{10\hat{i}+15\hat{j}+25\hat{k}}{2\hat{i}+3\hat{j}-5\hat{k}}m=\frac{\sqrt{{10}^2+{15}^2+{25}^2}}{\sqrt{2^2+3^2+5^2}}m=\frac{\sqrt{950}}{\sqrt{38}}m=\frac{5\sqrt{38}}{\sqrt{38}}=5units$

Hence, correct option is $\left(A\right)$