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NEET Physics QUESTION #1035
Question 1
Two inclined surfaces of equal length \(L\) at \(45°\): one rough, one smooth. A body takes 2 times longer on the rough surface. The coefficient of kinetic friction \(\mu_k\) is close to:
  • 0.5
  • 0.75✔️
  • 0.25
  • 0.40
Correct Answer Explanation
On smooth: \(a_s = g\sin45°\). On rough: \(a_r = g(\sin45°-\mu_k\cos45°)\). Time ratio: \(t_r/t_s=2\). Since \(L = \frac{1}{2}at^2\): \(t\propto 1/\sqrt{a}\). So \(\frac{t_r}{t_s}=\sqrt{\frac{a_s}{a_r}}=2\Rightarrow \frac{a_s}{a_r}=4\Rightarrow a_r=\frac{a_s}{4}\). \(g(\sin45°-\mu_k\cos45°)=\frac{g\sin45°}{4}\Rightarrow 1-\mu_k=\frac{1}{4}\Rightarrow \mu_k=0.75\).