Question:
A frictionless wire AB is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is
A frictionless wire AB is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is
Updated On: Jun 7, 2022
- $\frac{\sqrt{2gR}}{g\,cos\,\theta}$
- $2\sqrt{gR}. \frac{cos\,\theta}{g}$
- $2\sqrt{\frac{R}{g}}$
- $\frac{gR}{\sqrt{g\,cos\,\theta}}$
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Acceleration of body along AB is g cos ? Distance travelled in time t sec is
AB $=\frac{1}{2}$ (g cos ?)t
From ?ABC, AB = 2R cos ?
Thus, 2 R cos ? $\frac{1}{2}$ g cos ? t
$\Rightarrow t^{2}=\frac{4\,R}{g} \Rightarrow t=2\sqrt{\frac{R}{g}}$
AB $=\frac{1}{2}$ (g cos ?)t
From ?ABC, AB = 2R cos ?
Thus, 2 R cos ? $\frac{1}{2}$ g cos ? t
$\Rightarrow t^{2}=\frac{4\,R}{g} \Rightarrow t=2\sqrt{\frac{R}{g}}$
Was this answer helpful?
0
0
Top Questions on Motion in a straight line
- A bus moving along a straight highway with speed of 72 km/h is brought to halt within 4s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _______m.
- JEE Main - 2024
- Physics
- Motion in a straight line
- The displacement and the increase in the velocity of a moving particle in the time interval of \( t \) to \( (t + 1) \) s are 125 m and 50 m/s, respectively. The distance travelled by the particle in \( (t + 2)^{\text{th}} \) s is \( \_\_\_\_ \) m.
- JEE Main - 2024
- Physics
- Motion in a straight line
- Two cars are travelling towards each other at a speed of \( 20 \, \text{m/s} \) each. When the cars are \( 300 \, \text{m} \) apart, both the drivers apply brakes and the cars retard at the rate of \( 2 \, \text{m/s}^2 \). The distance between them when they come to rest is:
- JEE Main - 2024
- Physics
- Motion in a straight line
- A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity \(4\ ms^{-1}\). The ball strikes the water surface after \(4s\). The height of bridge above water surface is
(Take: \(g=10\ ms^{-2}\))- NEET (UG) - 2023
- Physics
- Motion in a straight line
- A bullet from a gun is fired on a rectangular wooden block with velocity u. When the bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes \(\frac{u}{3}\). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:
- NEET (UG) - 2023
- Physics
- Motion in a straight line
View More Questions
Questions Asked in JIPMER exam
- Binomial nomenclature was first introduced by
- JIPMER - 2015
- KCET - 2022
- Diversity In The Living World
- A convex lens $'A'$ of focal length $20\, cm$ and a concave lens $'B'$ of focal length $5\, cm$ are kept along the same axis with a distance $'d'$ between them. If a parallel beam of light falling on $'A'$ leaves $'B'$ as a parallel beam, then the distance $'d'$ in cm will be :
- JIPMER - 2021
- Spherical Mirrors
- A bacterial flagellum is composed of
- JIPMER - 2021
- Prokaryotic Cells
- $2,4-DNP $ test can be used to identify :
- JIPMER - 2021
- Chemical Reactions
- How many moles of acidified $K_2Cr_2O_7$ is required to liberate $6$ moles of $I_2$ from an aqueous solution of $I^-$ ?
- JIPMER - 2020
- Mole concept and Molar Masses
View More Questions
Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.