A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height \(\frac h3\) while going up and coming down respectively.
\(\frac {\sqrt 2-1}{\sqrt 2+1}\)
\(\frac {\sqrt 3-\sqrt 2}{\sqrt 3+\sqrt 2}\)
\(\frac{\sqrt 3-1}{\sqrt3+1}\)
\(\frac 13\)
The Correct Option is B
Solution and Explanation
Velocity, \(v=\sqrt {2gh}\)
\(\frac h3=\sqrt {2gh}t−\frac 12gt^2\)
\(\frac 12gt^2+\frac h3-\sqrt {2gh}t=0\)
\(\frac {t1}{t2}=\frac {\sqrt {2gh}+\sqrt {gh−2gh/3} }{\sqrt {2gh}−\sqrt {2gh−2gh/3}}\)
\(=\frac {\sqrt 2+\frac {2}{\sqrt 3} }{\sqrt 2−\frac {2}{\sqrt 3}}\)
\(=\frac {\sqrt 3-\sqrt 2}{\sqrt 3+\sqrt 2}\)
So, the correct option is (B): \(\frac {\sqrt 3-\sqrt 2}{\sqrt 3+\sqrt 2}\).
Top Questions on Motion in a straight line
- A ball is dropped from a height of 20 m. What is its velocity just before hitting the ground? (Take \( g = 9.8 \, \text{m/s}^2 \))
- VITEEE - 2025
- Physics
- Motion in a straight line
- A body of mass \( 5 \, \text{kg} \) is placed on a frictionless inclined plane of angle \( 30^\circ \). What is the component of the weight of the body along the plane?
- MHT CET - 2025
- Physics
- Motion in a straight line
- A car starts from rest and accelerates uniformly at 3 m/s\textsuperscript{2. What will be its velocity after 5 seconds?}
- MHT CET - 2025
- Physics
- Motion in a straight line
- A projectile is fired with an initial velocity of 20 m/s at an angle of 30\(^\circ\) with the horizontal. Calculate the maximum height reached by the projectile.
- MHT CET - 2025
- Physics
- Motion in a straight line
- A 5 kg block is placed on a horizontal surface. A force of 10 N is applied to the block. The coefficient of friction between the block and the surface is 0.2. Find the acceleration of the block.
- MHT CET - 2025
- Physics
- Motion in a straight line
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:
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.