Question

An object takes 1 second to slide down a rough ${45}^o$ inclined plane. The time taken to slide down a smooth ${30}^o$ inclined plane having the same slope length is $(\mu =0.5)$

• A. $\sqrt{2}s$
• B. $\frac{1}{2}s$
• C. $\frac{1}{2\sqrt{2}}s$
• D. $2^{-1/4}s$

Answer 1

Answer: (D)

$2^{-1/4}s$

$t=1seca=gsin45-\mu gcos45g(\frac{1}{\sqrt{2}}-\frac{1}{2\sqrt{2}})=\frac{g}{\sqrt{2}}\left(\frac{1}{2}\right)=\frac{g}{2\sqrt{2}}s=\frac{g}{\sqrt{2}}\left(\frac{1}{2}\right)\times 1^2=\frac{g}{4\sqrt{2}}ma=gsin30=\frac{g}{2}t=2^{-\frac{1}{4}}sec$