Question

If F is the force, S is the displacement and V is the velocity of the particle, the dimensions of the ratio $FS/V^{2}$ will be}

• A. $M^{0}LT^{0}$
• B. $M^{1}L^{0}T^{0}$
• C. $M^{0}L^{0}T$
• D. $M^{0}L^{0}T^{0}$

Hint:

$FS$ represents Work (Energy), and Kinetic Energy is $\frac{1}{2}mv^{2}$. Thus, $FS/V^{2}$ must have the dimensions of Mass ($M$).

Answer 1

The Correct Option is B

Step 1: Concept
The dimensions of physical quantities are: Force ($F$) = [$MLT^{-2}$], Displacement ($S$) = [$L$], and Velocity ($V$) = [$LT^{-1}$].

Step 2: Meaning
We need to find the dimensional formula of the expression $\frac{F \times S}{V^{2}}$.

Step 3: Analysis
Substitute the dimensions: $\frac{[MLT^{-2}] \times [L]}{[LT^{-1}]^{2}} = \frac{[ML^{2}T^{-2}]}{[L^{2}T^{-2}]}$.

Step 4: Conclusion
Simplifying the expression leads to $[M^{1}L^{0}T^{0}]$, which is the dimension of mass. Final Answer: (B)