A ball of mass (m) 0.5 kg is attached to the end of a string having length (l) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rad/s) is
- 9
- 18
- 27
- 36
The Correct Option is D
Solution and Explanation
$T \sin \theta$ component will provide necessary centripetal force to the ball towards centre $C$
$\therefore\, T \sin \theta =mr \omega^2=m(l \sin \theta)\omega^2\, $ or $T=m l \omega^2$
$\therefore 15mm \omega=\sqrt{\frac{T}{ml}}$
or $15mm \omega_{max}=\sqrt{\frac{T_{max}}{ml}}=\sqrt{\frac{324}{0.5\times 0.5}}$
$25mm = 36\, rad/s $
$\therefore $ Correct option is (d)
Top Questions on laws of motion
- Two blocks of masses 8 kg and 12 kg kept on a smooth horizontal table are connected to the ends of a light string as shown in the figure. If a horizontal force of 500 N is applied to the block of mass 12 kg, then the tension in the string connecting the blocks is
- AP EAPCET - 2025
- Physics
- laws of motion
- A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. What is the car's acceleration?
- MHT CET - 2025
- Physics
- laws of motion
- Two balls each of mass 250 g moving in opposite directions each with a speed 16 m/s collide and rebound with the same speeds. The impulse imparted to one ball due to the other is
- AP EAPCET - 2025
- Physics
- laws of motion
- A body of mass 2 kg starts moving from the origin (0, 0) with an initial velocity of \( (4\hat{i} + 4\hat{j})\ \text{ms}^{-1} \). A constant force of \( -20\hat{j} \ \text{N} \) is applied on the body. When the Y-coordinate of the position of the body becomes zero again, then its X-coordinate is
- AP EAPCET - 2025
- Physics
- laws of motion
- A body A of mass 200 g moving with a velocity \(\vec{v}_1 \hat{i}\) makes collision with another body B of mass 100 g moving with a velocity \(\vec{v}_2 \hat{i}\). After collision, A and B move with velocities \(\vec{v}_3 \hat{i}\) and \(\vec{v}_4 \hat{i}\) respectively. If \(v_3 = 0.5v_1\), then the value of \(v_1\) is
- AP EAPCET - 2025
- Physics
- laws of motion
Questions Asked in JEE Advanced exam
- Let $ x_0 $ be the real number such that $ e^{x_0} + x_0 = 0 $. For a given real number $ \alpha $, define $$ g(x) = \frac{3xe^x + 3x - \alpha e^x - \alpha x}{3(e^x + 1)} $$ for all real numbers $ x $. Then which one of the following statements is TRUE?
- JEE Advanced - 2025
- Fundamental Theorem of Calculus
- At 25$^\circ$C, the concentration of H$^+$ ions in $ 1.00 \times 10^{-3} \, \text{M} $ aqueous solution of a weak monobasic acid having acid dissociation constant $ K_a = 4.00 \times 10^{-11} $ is $ X \times 10^{-7} \, \text{M} $. The value of $ X $ is ____. {Use: Ionic product of water $ K_w = 1.00 \times 10^{-14} $ at 25$^\circ$C
- JEE Advanced - 2025
- Ionic Equilibrium
- Consider the vectors $$ \vec{x} = \hat{i} + 2\hat{j} + 3\hat{k},\quad \vec{y} = 2\hat{i} + 3\hat{j} + \hat{k},\quad \vec{z} = 3\hat{i} + \hat{j} + 2\hat{k}. $$ For two distinct positive real numbers $ \alpha $ and $ \beta $, define $$ \vec{X} = \alpha \vec{x} + \beta \vec{y} - \vec{z},\quad \vec{Y} = \alpha \vec{y} + \beta \vec{z} - \vec{x},\quad \vec{Z} = \alpha \vec{z} + \beta \vec{x} - \vec{y}. $$ If the vectors $ \vec{X}, \vec{Y}, \vec{Z} $ lie in a plane, then the value of $ \alpha + \beta - 3 $ is ________.
Two identical concave mirrors each of focal length $ f $ are facing each other as shown. A glass slab of thickness $ t $ and refractive index $ n_0 $ is placed equidistant from both mirrors on the principal axis. A monochromatic point source $ S $ is placed at the center of the slab. For the image to be formed on $ S $ itself, which of the following distances between the two mirrors is/are correct:
- JEE Advanced - 2025
- Ray optics and optical instruments
- Let $$ \alpha = \frac{1}{\sin 60^\circ \sin 61^\circ} + \frac{1}{\sin 62^\circ \sin 63^\circ} + \cdots + \frac{1}{\sin 118^\circ \sin 119^\circ}. $$ Then the value of $$ \left( \frac{\csc 1^\circ}{\alpha} \right)^2 $$ is \rule{1cm}{0.15mm}.
- JEE Advanced - 2025
- Some Applications of Trigonometry
JEE Advanced Notification
Concepts Used:
Laws of Motion
The laws of motion, which are the keystone of classical mechanics, are three statements that defined the relationships between the forces acting on a body and its motion. They were first disclosed by English physicist and mathematician Isaac Newton.
Newton’s First Law of Motion
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion
Newton's 2nd law of motion deals with the relation between force and acceleration. According to the second law of motion, the acceleration of an object as built by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Newton’s Third Law of Motion
Newton's 3rd law of motion states when a body applies a force on another body that there is an equal and opposite reaction for every action.