A block of mass 2 kg moving on a horizontal surface with speed of 4 ms–1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = –kx where k = 12 Nm–1. The speed of the block as it just crosses the rough surface will be
- Zero
1.5 ms–1
2.0 ms–1
2.5 ms–1
The Correct Option is C
Solution and Explanation
Given: \(k=12 Nm^{-1}\)
\(F = –kx\)
\(F = –12x\)
\(mv \text{} \frac{dv}{dx} =−12\)
\(\int_{4}^{v}vdx=-6\int_{0.5}^{1.5}xdx\)
(m = 2 kg)
\(\frac{v^2-16}{2}\)=−6[\(\frac{1.5^2-0.5^2}{2}\)]
\(\frac{v^2 -16}{2}\)=−6
v = 2 m/sec
\(\therefore ,\) The correct option is (C): \(2.0\text{ ms}^{-1}\)
Top Questions on Friction
- A 10 kg box is pulled with a horizontal force of 50 N on a surface offering a frictional force of 20 N. What is the net acceleration of the box? (Take \( g = 10 \, \text{m/s}^2 \))
- There are two inclined surfaces of equal length inclined at an angle of \(45^\circ\) with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on the rough surface than on the smooth surface. The coefficient of kinetic friction (\(\mu_k\)) between the object and the rough surface is close to :
- A block of mass 5 kg is placed on a frictionless surface and pushed with a force of 20 N at an angle of 30° to the horizontal. What is the acceleration of the block?
- Choose the correct statement
- A block of mass \( 5 \, \text{kg} \) is placed on a horizontal surface. The coefficient of friction between the block and the surface is \( 0.4 \). What is the force of friction acting on the block?
Questions Asked in JEE Main exam
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
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
Concepts Used:
Types of Friction
There exists a force called friction which works against the motion between two surfaces that are in contact. Multiple types of friction have been identified, such as static friction, kinetic friction, rolling friction, and fluid friction.
Static friction is the force that opposes the initiation of motion between two surfaces in contact that are not moving relative to each other. It is generally greater than the force of kinetic friction, which is the force that opposes the motion of two surfaces that are in contact and are moving relative to each other. The force of kinetic friction is proportional to the normal force, which is the force perpendicular to the contact surface.
Rolling friction occurs when an object rolls over a surface, such as a wheel rolling on a road. The force of rolling friction is generally less than the force of kinetic friction, which makes it more efficient for transportation.
When an object moves through a fluid like water or air, it experiences fluid friction. The force of fluid friction depends on the object's speed, size, and shape, as well as the properties of the fluid, such as its viscosity.
Also Read: Friction Force Formula
Friction is a fundamental force that affects many aspects of our lives, including transportation, construction, and manufacturing. Understanding the types of friction and their properties is essential for designing and optimizing machines and structures that rely on frictional forces for their function.