Question

A body of mass
'm' slides down a smooth inclined plane
having an inclination of 45° with the horizontal. It takes
2s to reach the bottom. If the body is placed on a similar
plane having coefficient friction 0.5, what is the time taken for it to reach the bottom?
​

Answer 1

Given :-

• A body of mass m slides down a smooth inclined plane having an inclination of 45° with the horizontal. It takes the body 2 seconds to reach the bottom.

To Find :-

• Time taken by the body if the coefficient of friction of the plane is 0.5

Solution :-

• Let's find the distance travelled by the body using the first case. Since the plane is smooth in this case, So there will be no frictional force opposing the motion of the body down the inclined plane.

• So, Acceleration with the incline is g sin θ,
• Using second equation of motion,

⇒ s = ut + 1/2 at²

⇒ s = 1/2 × g sin θ × 2²

⇒ s = 2 × 10 × sin 45°

⇒ s = 20 × 1/√2

⇒ s = 10√2 units.

• In the second case, we have friction, So it will oppose the motion of body,

Here, The acceleration would become

⇒ g sin θ - μ g cos θ

⇒ 10×sin 45° - 0.5 × 10 × cos 45°

⇒ 5√2 - 5√2 / 2

⇒ ( 10√2 - 5√2 ) / 2

⇒ 5√2/2 unit/s²

• Now, Let us find the time taken by the body to cover 10√2 unit.

Using second equation of motion,

⇒ s = ut + 1/2 at²

⇒ 10√2 = 1/2 × 5√2 / 2 × t²

⇒ 10√2 = 5√2 / 4 × t²

⇒ 40√2 / 5√2 = t²

⇒ 8 = t²

⇒ t = 2√2 seconds

Hence, The body will take 2√2 seconds.

Answer 2

Answer:

Full answer with explanation is in above given images..