Gujarati
Hindi
4-1.Newton's Laws of Motion
normal

Starting from rest a body slides down a $45^{\circ}$ ind ined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is:

A

$0.33$

B

$0.25$

C

$0.75$

D

$0.80$

Solution

Let length is $\ell$ of inclined plane, then $f_r=\mu N =\mu mg \cos \theta$

$mg \sin \theta- f _{ r }= ma$

$mg \sin \theta-\mu mg \cos \theta= ma$

Now

$\ell=\frac{1}{2} at ^2=\frac{1}{2} g (\sin \theta-\mu \cos \theta) t ^2$

$\text { Now } \ell_1=\ell_2$

$\ell_2=\frac{1}{2} g \sin \theta\left(\frac{ t ^2}{2}\right)$

$\frac{1}{2} g(\sin \theta-\mu \cos \theta) t ^2=\frac{1}{2} g(\sin \theta-0 \times \cos \theta)\left(\frac{ t ^2}{2}\right)$

$4(\sin \theta-\mu \cos \theta)=\sin \theta$

$\mu=\frac{3}{4}=0.75$

Standard 11
Physics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.