In the equation P=(a−t³)/(bL²), P denotes pressure, t denotes time, and L denotes distance. Find the sum of time-dimension exponents of a and b.
Physics · Mixed Chapter
JEE Main Practice

Question

In the equation P=(a−t³)/(bL²), P denotes pressure, t denotes time, and L denotes distance. Find the sum of time-dimension exponents of a and b.

G1 Physics · Accepted Answer

Step 1: Dimensional homogeneity of (a−t³) requires [a]=T³, so time exponent of a is 3. Step 2: Rearranging b=(a−t³)/(PL²), with [P]=ML⁻¹T⁻². Step 3: [b]=T³/[MLT⁻²]=M⁻¹L⁻¹T⁵, so time exponent of b is 5. Step 4: Sum=3+5=8. The PDF says “value of Z” but its answer 8 corresponds to sum for a and b.