A person is driving a vehicle at uniform speed of `5 m s^(-1)` on a level curved track of radius 5m. The coefficient of static friction between tyres and road is 0.1. Will the person slip while taking the turn with the same speed ? Take `g=10 ms^(-2)`.
Choose the correct statement.

Options

A. A person will slip if `v^(2) lt 5 ms^(-1)`.
B. A person will slip if `v^(2) = 5 ms^(-1)`.
C. A person will slip if `v^(2) gt 10 ms^(-1)`.
D. A person will slip if `v^(2) gt 5 ms^(-1)`.

Answer

D

Explanation

The person will not slip if
`v^(2) le mu_(s) Rg`
Here, `mu_(s)=0.1, R=5m, g=10ms^(-2)`
`:.mu_(s)Rg=0.1xx5 m xx 10 ms^(-2)=5m^(2)s^(-2)`
or `v^(2)le 5 m^(2)s^(-2)`
Therefore the person will slip if `v^(2) gt 5m^(2)s^(-2)`.
Note: In the question paper the unit of `v^(2)` is given to be m `s^(-1)`. But if is wrong. It is a unit of v not `v^(2)`. The correct unit of `v^(2)`. The correct unit of `v^(2)` is `m^(2) s^(-2)`.