Question

If \(E =\) energy, \(G =\) gravitational constant, \(I =\) impulse and \(M =\) mass, then dimensions of \( \frac{EI}{GM^2} \) are same as that of:

• A. \( \text{time} \)
• B. \( \text{mass} \)
• C. \( \text{length} \)
• D. \( \text{force} \)

Hint:

Always reduce dimensions step-by-step by cancelling powers carefully.

Answer 1

The Correct Option is A

Concept: Dimensional formula:
•Energy: \( [E] = ML^2T^{-2} \)
•Impulse: \( [I] = MLT^{-1} \)
•Gravitational constant: \( [G] = M^{-1}L^3T^{-2} \)
•Mass: \( [M] = M \)

Step 1:Write dimensions:} \[ \frac{EI}{GM^2} = \frac{(ML^2T^{-2})(MLT^{-1})}{(M^{-1}L^3T^{-2})(M^2)} \]

Step 2:Simplify:} \[ = \frac{M^2L^3T^{-3}}{ML^3T^{-2}} = MT^{-1} \]

Step 3:Final dimension:} \[ = T \] Hence, it represents time.