A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of 4 m/s, is ______ cm. (Take g = 10 m/s2).
Fig.
A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of 4 m/s, is ______ cm. (Take g = 10 m/s2).
Correct Answer: 120
Solution and Explanation
The correct answer is 120
\(α = \frac{(mg)(r)}{\frac{3}{2}mr^2} = \frac{2g}{3r}\)
\(⇒ a = \frac{2g}{3}\)
\(⇒ v^2 = 2as\)
\(16 = \frac{40}{3}×s\)
⇒ s = 0.3×4
= 120cm
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
Questions Asked in JEE Main exam
Let \[ I(x) = \int \frac{dx}{(x-11)^{\frac{11}{13}} (x+15)^{\frac{15}{13}}} \] If \[ I(37) - I(24) = \frac{1}{4} \left( b^{\frac{1}{13}} - c^{\frac{1}{13}} \right) \] where \( b, c \in \mathbb{N} \), then \[ 3(b + c) \] is equal to:
- JEE Main - 2025
- Integration
- Given below are two statements: Statement I: One mole of propyne reacts with excess of sodium to liberate half a mole of H₂ gas. Statement II: Four g of propyne reacts with NaNH₂ to liberate NH₃ gas which occupies 224 mL at STP. In the light of the above statements, choose the most appropriate answer from the options given below:
- JEE Main - 2025
- Organic Chemistry
- Given below are two statements about X-ray spectra of elements:
Statement (I):A plot of \(\sqrt {v}\) (v=frequency of X-rays emitted) vs atomic mass is a straight line.
Statement (II): A plot of v (v=frequency of X-rays emitted)} vs atomic number is a straight line.- JEE Main - 2025
- X-ray Spectra and Moseley's Law
For the thermal decomposition of \( N_2O_5(g) \) at constant volume, the following table can be formed, for the reaction mentioned below: \[ 2 N_2O_5(g) \rightarrow 2 N_2O_4(g) + O_2(g) \] Given: Rate constant for the reaction is \( 4.606 \times 10^{-2} \text{ s}^{-1} \).
- JEE Main - 2025
- Organic Chemistry
- The ratio of the power of a light source \( S_1 \) to that of the light source \( S_2 \) is 2. \( S_1 \) is emitting \( 2 \times 10^{15} \) photons per second at 600 nm. If the wavelength of the source \( S_2 \) is 300 nm, then the number of photons per second emitted by \( S_2 \) is \_\_\_\_\_ \( \times 10^{14} \).
- JEE Main - 2025
- Units and measurement
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)