Home
Class 11
PHYSICS
What is the full form of SI? a) Standar...

What is the full form of SI?
a) Standard International
b) System International
c) Scientific International
d) Science International

Text Solution

Verified by Experts

Let P bet he force applied to it an angle `theta` From the free body diagram,
`R+P isn theta -mg=0`
`rarr R=-Psin theta+mg`……….i
`muR=Pcostheta `……….ii
From equation i
`mu(mg-Psintheta)-Pcostheta`
`mumg=muPsintheta-Pcostheta`
`rarr P=(mu mg)/(musintheta+costheta)`
Applied force Pshould be minimum, when `m sintheta+costheta` is maximum.
Again `(musintheta+costheta)` is maximum when its derivative is zero
`d/(dtheta) (mu sintheta+costheta)=0` rarr mucostheta-sintheta=0`
rarr `theta=tan^-1 mu`
So, `P=(mumg)/(musintheta+costheta)`
`=(mumg/costheta)/((musintheta)/(costheta)+(costheta)/(costheta))`

(Dividing Numerator and DenomiN/Ator by `costheta), we get
`P=(mumgsectheta)/(1+mutantheta)`
`(mu mgsectheta)/(1+tan^2theta)=(mumg)/(sectheta)`
`=(mumg)/(sqrt(1+tan^2theta)(mu mg)/(1+mu^2)`
Hence minimum fore is `mu(mg)/(sqrt(1+mu^2)` at an angle `theta=tan^-1mu`
Promotional Banner

Similar Questions

Explore conceptually related problems

Write a note on SI (System International)

What is the internal energy of a system ?

Does the international space station have gravitational potential energy

What is total internal reflection ?

Write condition for total internal reflection.

Explain internal reflection and total internal reflection.

External fertilization and Internal fertilization.