In F = a√x + bt², where F is force, x is distance and t is time, [a/b] = L⁻¹⁄²Tⁿ. Find n.
Physics · Mixed Chapter
JEE Main Practice

Question

In F = a√x + bt², where F is force, x is distance and t is time, [a/b] = L⁻¹⁄²Tⁿ. Find n.

G1 Physics · Accepted Answer

Step 1: [F] = MLT⁻² and [√x] = L¹⁄². Thus [a] = [F]/L¹⁄² = ML¹⁄²T⁻². Step 2: Since [bt²] = [F], [b] = MLT⁻⁴. Step 3: [a/b] = (ML¹⁄²T⁻²)/(MLT⁻⁴) = L⁻¹⁄²T². Therefore n = 2.