NEET 2025 — Physics solution

NEET2025Physics

There are two inclined surfaces of equal length ( $L$ ) and same angle of inclination $4 5^{\circ}$ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes $2$ times as much time to slide down on the rough surface than on the smooth surface. The coefficient of kinetic friction ( $μ_{k}$ ) between the object and the rough surface is close to:

A
0.25
B
0.40
C
0.5
D
0.75

Solution

Acceleration on smooth incline: $a_{S} = g sin θ$ . Acceleration on rough incline: $a_{R} = g sin θ - μ_{k} g cos θ$ .

Length is the same, and from $L = \frac{1}{2} a t^{2}$ we get $\frac{t _{S}^{2}}{t _{R}^{2}} = \frac{a _{R}}{a _{S}}$ . Given $t_{R} = 2 t_{S}$ , so $\frac{1}{4} = \frac{a _{R}}{a _{S}}$ .

At $θ = 4 5^{\circ}$ , $sin θ = cos θ = \frac{1}{2}$ , so $\frac{1}{4} = \frac{1 - μ _{k}}{1}$ , giving $μ_{k} = 1 - \frac{1}{4} = 0.75$ .

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