The potential energy of a particle moving along x-direction varies as V = Px²/(√x + Q). The dimensions of P²/Q are:
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The potential energy of a particle moving along x-direction varies as V = Px²/(√x + Q). The dimensions of P²/Q are:

G1 Physics · Accepted Answer

Step 1: Because √x and Q are added, they must have the same dimensions. Since [x] = [L], [√x] = [L¹ᐟ²], so [Q] = [L¹ᐟ²]. Step 2: Potential energy has dimensions [M L² T⁻²]. From V = Px²/(√x + Q), [P][L²]/[L¹ᐟ²] = [M L² T⁻²], hence [P] = [M L¹ᐟ² T⁻²]. Step 3: [P²/Q] = [M² L T⁻⁴]/[L¹ᐟ²] = [M² L¹ᐟ² T⁻⁴]. Final answer: C.