Question:
A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ $ms ^{-1}$(Given $g =10 \,ms ^{-2}$ )
A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ $ms ^{-1}$(Given $g =10 \,ms ^{-2}$ )
Updated On: Mar 19, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 2
Solution and Explanation
\[ v = \sqrt{\frac{2gh}{1 + \frac{k^2}{R^2}}} \] Where \( h = 60 \sin 30^\circ = 30 \) cm \[ k^2 = \frac{R^2}{2} \] \[ v = 2 \text{ ms}^{-1} \]
Was this answer helpful?
3
1
Top Questions on Rotational motion
- A thin spherical shell of radius \( 0.5 \, \text{m} \) and mass \( 2 \, \text{kg} \) is rotating about its axis of symmetry with an angular velocity of \( 10 \, \text{rad/s} \). What is its moment of inertia?
- MHT CET - 2025
- Physics
- Rotational motion
- If the displacement of a particle executing simple harmonic motion is given by \( x = 0.5 \cos(125.6\,t) \), then the time period of oscillation of the particle is nearly (Here \(x\) is displacement in metre and \(t\) is time in second)
- AP EAPCET - 2025
- Physics
- Rotational motion
- The apparent weight of a girl of mass 30 kg when she is in a lift moving vertically upwards with an acceleration of \( 2~\text{ms}^{-2} \) is
(Acceleration due to gravity = \( 10~\text{ms}^{-2} \))- AP EAPCET - 2025
- Physics
- Rotational motion
- A solid sphere and a solid cylinder have same mass and same radius. The ratio of the moment of inertia of the solid sphere about its diameter and the moment of inertia of the solid cylinder about its axis is:
- AP EAPCET - 2025
- Physics
- Rotational motion
- If the velocity at the maximum height of a projectile projected at an angle of \(45^\circ\) is \(20 \, \text{m/s}\), then the maximum height reached by the projectile is:
- AP EAPCET - 2025
- Physics
- Rotational motion
View More Questions
Questions Asked in JEE Main exam
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
- JEE Main - 2025
- Relations and functions
- If \( \alpha + i\beta \) and \( \gamma + i\delta \) are the roots of the equation \( x^2 - (3-2i)x - (2i-2) = 0 \), \( i = \sqrt{-1} \), then \( \alpha\gamma + \beta\delta \) is equal to:
- JEE Main - 2025
- Complex numbers
- The sum of all local minimum values of the function \( f(x) \) as defined below is:
\[ f(x) = \begin{cases} 1 - 2x & \text{if } x < -1, \\[10pt] \frac{1}{3}(7 + 2|x|) & \text{if } -1 \leq x \leq 2, \\[10pt] \frac{11}{18}(x-4)(x-5) & \text{if } x > 2. \end{cases} \]- JEE Main - 2025
- Functions
- Let \( \langle a_n \rangle \) be a sequence such that \( a_0 = 0 \), \( a_1 = \frac{1}{2} \), and \( 2a_{n+2} = 5a_{n+1} - 3a_n \).n= 0,1,2,3.... Then \( \sum_{k=1}^{100} a_k \) is equal to:
- JEE Main - 2025
- Sequences and Series
- The expression given below shows the variation of velocity \( v \) with time \( t \): \[ v = At^2 + \frac{Bt}{C + t}. \] The dimension of \( ABC \) is:
- JEE Main - 2025
- Thermodynamics terms
View More Questions
Concepts Used:
Rotational Motion
Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.
Rotational Motion Examples:
The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.
Other examples:
- Moving by Bus
- Sailing of Boat
- Dog walking
- A person shaking the plant.
- A stone falls straight at the surface of the earth.
- Movement of a coin over a carrom board
Types of Motion involving Rotation:
- Rotation about a fixed axis (Pure rotation)
- Rotation about an axis of rotation (Combined translational and rotational motion)
- Rotation about an axis in the rotation (rotating axis)