Question

# A block of mass m takes time t to slide down on a smooth inclined plane of angle of inclination θ and height h. If same block slides down on a rough inclined plane of same angle of inclination and same height and takes time n times of initial value, then coefficient friction between block and inclined plane is

A
[1+n2]tanθ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
[11n2]tanθ
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
[1n2]tanθ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
[1+1n2]tanθ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B [1−1n2]tanθWhen an object is sliding down the incline plane of height h and inclination θthen total length of the inclined plane is L=hsinθAlso the acceleration on the smooth inclined plane will bea=gsinθnow we have time to slide downt=√2×Lat=1sinθ√2×hgnow when it slide down the rough plane the acceleration will be less due to friction forcenow in that case acceleration is given bya=sinθ−μgcosθagain by above formulat′=1sinθ√2×hg(1−μtanθ)given that the on rough plane is n time more than the smooth plane.t′=nt1sinθ√2×hg(1−μtanθ)=n×1sinθ√2×hgg(1−μtanθ)=gn2so, friction coefficient is given byμ=1tanθ(1−1n2)

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Second Law of Motion
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program