Question

Starting from rest, a body slides down a 45° inclined 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​

Answer 1

Answer:

The body is circular whereas the inclined plane is flat at 45°.

Explanation:

This is because it is taking twice the time. Which means a flat surface will the the once time. In this case we need a round object for example ball. There is no friction on the inclined plane, which means the inclined plane is soapy or oily.

Answer 2

When there is no friction.

Let distance traveled = x

F = ma

mg SinØ = ma

a = gSinØ

X = 1/2at²

2x = gSinØt²

t = √2x/gSinØ -------(1)

When there is Friction.

F - f = ma'

mgSinØ - μmg CosØ = ma'

a' = (gSinØ - μg CosØ)

Since, Distance traveled is same.

X = 1/2a't'²

t' = √2x/gSinØ - μgCosØ -----(2)

As given,

t' = 2t

√2x/gSinØ - μgCosØ = 2√2x/gSinØ

Squaring both sides.

2x/gSinØ - μgCosØ = 4×2x/gSinØ

1/g(SinØ- μgCosØ) = 4/gSinØ

Putting, Ø = 45°

1/(1/√2 - μ/√2) = 4√2

√2/1 - μ = 4√2

4 - 4μ = 1

-4μ = -3

μ = 3/4

μ = 0.75