Question:
If the dimensional formula of
\[
(\text{Energy} \times \text{speed})
\]
is
\[
[M^aL^bT^c],
\]
then \(a,b,c\) are:
If the dimensional formula of
\[
(\text{Energy} \times \text{speed})
\]
is
\[
[M^aL^bT^c],
\]
then \(a,b,c\) are:
Show Hint
When multiplying physical quantities, add the powers of corresponding dimensions.
Updated On: Jun 24, 2026
- \((1,3,-3)\)
- \((1,2,2)\)
- \((1,2,3)\)
- \((1,3,-2)\)
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Write the dimensional formula of energy.
Dimensional formula of energy is \[ [ML^2T^{-2}] \]
Step 2: Write the dimensional formula of speed.
Dimensional formula of speed is \[ [LT^{-1}] \]
Step 3: Multiply the dimensions.
\[ (\text{Energy} \times \text{speed}) = [ML^2T^{-2}]\times [LT^{-1}] \] \[ =[ML^3T^{-3}] \] Thus, \[ a=1,\quad b=3,\quad c=-3 \]
Step 4: Final conclusion.
Hence, \[ \boxed{(1,3,-3)} \]
Dimensional formula of energy is \[ [ML^2T^{-2}] \]
Step 2: Write the dimensional formula of speed.
Dimensional formula of speed is \[ [LT^{-1}] \]
Step 3: Multiply the dimensions.
\[ (\text{Energy} \times \text{speed}) = [ML^2T^{-2}]\times [LT^{-1}] \] \[ =[ML^3T^{-3}] \] Thus, \[ a=1,\quad b=3,\quad c=-3 \]
Step 4: Final conclusion.
Hence, \[ \boxed{(1,3,-3)} \]
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