A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination 30°. The centre of mass of cylinder has speed of 4 m/s. The distance travelled by the cylinder on the incline surface will be :
(Take g = 10 m/s\(^2\))
(Take g = 10 m/s\(^2\))
- 2.2 m
- 1.6 m
- 1.2 m
- 2.4 m
The Correct Option is D
Solution and Explanation
\(\frac{1}{2} mv^2 ( 1 + \frac{K^2}{R^2}) = mgh\)
\(\Rightarrow 8 ( 1 + \frac{1}{2}) = 10\,h\)
\(h = 1.2\,m\)
\(\frac{h}{l} = sin\,30^{\circ}\)
\(l = 2.4 \,m\)
So, the correct option is (D): 2.4 m
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.