Question

49 A block of mass m is released on the top of a smooth inclined plane
of length x and inclination as shown in figure. Horizontal surface is
rough. If block comes to rest after moving a distance d on the
horizontal surface, then coefficient of friction between block and
surface is
x sino
(1)
20
X COSO
2d
(2)
2d
X sino
(3) * sino
X COSO
(4)
d​

Answer 1

Answer: option 3

Explanation:

Answer 2

Answer:

3.$\frac{xsin\theta}{d}$

Explanation:

We are given that mass of block is m and released on the top of a smooth inclined plane of length x .

Distance traveled by block=d

We have to find the coefficient of friction between block and surface

Let h be the height of block from the ground.

From triangle

$\frac{h}{x}=sin\theta$

$h=xsin\theta$

At ground K.E=Gravitational potential energy at top  =mgh=$mg xsin\theta$

Friction force=$\mu mg$

Work done by friction force=K.E

$\mu mgd=mgxsin\theta$

$\mud=xsin\theta$

$\mu=\frac{x sin\theta}{d}$

Hence, the coefficient of friction =$\frac{xsin\theta}{d}$

Option 3 is true.

Answer:3.$\frac{xsin\theta}{d}$