Two equal positive point charges are separated by a distance $2 a$ The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $q_0$ becomes maximum is $\frac{a}{\sqrt{x}}$ The value of $x$ is ______
Correct Answer: 2
Solution and Explanation
The correct answer is 2
\(F=\frac{2Kqq_0x}{(x^2+a^2)^{3/2}}\)
For F to be maximum
\(\frac{dF}{dx}=0\)
\(x=\frac{a}{\sqrt2}\)
So, the correct answer is \(\frac{a}{\sqrt2}\)
Top Questions on distance and displacement
- Displacement \( s \) of a particle at time \( t \) is expressed as \( s = 2t^3 - 9t \). Find the acceleration at the time when the velocity vanishes.
- AP EAMCET - 2024
- Mathematics
- distance and displacement
- 100 Vernier scale divisions match with 99 main scale divisions of a slide caliper. If the value of each main scale division is 1 mm, then the Vernier constant is:
- OJEE - 2024
- Physics
- distance and displacement
- The velocity of a particular mass \( m \) is \( \vec{v} = 5 \hat{i} + 4 \hat{j} + 6 \hat{k} \) when at \( \vec{r} = -2 \hat{i} + 4 \hat{j} + 6 \hat{k} \). The angular momentum of the particle about the origin is:
- OJEE - 2024
- Physics
- distance and displacement
- The position-time graphs for two students A and B returning from school to their homes are shown in the figure.
A. A lives closer to the school
B. B lives closer to the school
C. A takes lesser time to reach home
D. A travels faster than B
E. B travels faster than A
Choose the correct answer from the options given below :- JEE Main - 2023
- Physics
- distance and displacement
A person moved from A to B on a circular path as shown in figure If the distance travelled by him is 60 m, then the magnitude of displacement would be Given ( Cos 135° = -0.7)
- JEE Main - 2022
- Physics
- distance and displacement
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
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.