The terminal velocity (
Vt) of a spherical body falling through a liquid is directly proportional to the square of its radius (
r2):
Vt∝r2.
The percentage error in terminal velocity can be calculated using the formula:
VtΔVt=2⋅rΔr.
Given:
r=5mm,Δr=0.1mm.
Substitute the values:
VtΔVt×100=2⋅rΔr×100=2⋅50.1⋅100=4%.
Hence, Assertion A is true.
However, the Reason R states that the terminal velocity is inversely proportional to the radius, which is incorrect because
Vt∝r2. Therefore, Reason R is false.
Thus, the correct answer is
(3).