Question

an object is placed on an inclined plane starts slide when the incline angle becomes 30 degree. the coefficient of static friction between the object and the plane is

Answer 1

Given :

▪ An object is placed on the rough inclined plane.

▪ Object starts slide down when the incline angle becomes 30°.

To Find :

▪ Co-efficient of friction b/w the object and plane.

Diagram :

↗ Please, see the attachment for better understanding.

SoluTion :

☞ Just before sliding down,

$\dashrightarrow\sf\:mg\sin\theta=\mu\times N\\ \\ \dashrightarrow\sf\:mg\sin\theta=\mu\times mg\cos\theta\\ \\ \dashrightarrow\sf\:\mu=\dfrac{mg\sin\theta}{mg\cos\theta}\\ \\ \dashrightarrow\sf\:\mu=\tan\theta\\ \\ \dashrightarrow\sf\:\mu=\tan30\degree\\ \\ \dashrightarrow\underline{\boxed{\bf{\purple{\mu=\dfrac{1}{\sqrt{3}}=0.57}}}}\:\orange{\bigstar}$

Answer 2

${\bold{\huge{\underline{\orange{\underline{ANSWER:-}}}}}}$

$\bigstar\:\underline{\boxed{\bf{\green{CONCEPT}:}}}$

✔️when an object starts sliding at some angle “${theta}$” , then there are two forces will acts , i.e

• force of gravity and frictional force

such that,

• F = mg sin${theta}$
• N (Normal) = mg cos${theta}$

☞FORMULA:-

• F = k×N
• where , k = co-efficient of static friction.
• and N = Normal acting on the object .

☞GIVEN:-

• inclination angle(theta) = 30°

☞SOLUTION:-

• suppose mass of object is “m”.

✔️F = k × N

=> mg sin${theta}$ = k × mg cos${theta}$

=> k = sin(30°)/cos(30°)

=> k = (1/√3) .

$\bigstar\:\underline{\boxed{\bf{\red{Required Answer:k\:=\:1/✓3}}}}$