Put a uniform meter scale horizontally on your extended index fingers with the left one at $0.00 \,cm$ and the right one at $90.00 \,cm$.When you attempt to move both the fingers slowly towards the center, initially only the left finger slips with respect to the scale and the right finger does not. After some distance, the left finger stops and the right one starts slipping. Then the right finger stops at a distance $x_{R}$ from the center $(50.00 \,cm )$ of the scale and the left one starts slipping again. This happens because of the difference in the frictional forces on the two fingers. If the coefficients of static and dynamic friction between the fingers and the scale are $0.40$ and $0.32$, respectively, the value of $x_{R}$ (in $cm$ ) is____.
Correct Answer: 25.6
Solution and Explanation
The value of $x_{R}$ (in $cm$ ) is \(\underline{25.60}.\)
Top Questions on Friction
- A block of mass 2 kg is placed on a rough inclined plane at an angle of 30 degrees. The coefficient of friction between the block and the plane is 0.2. If the block is released from rest, will it slide down the plane? Justify your answer with calculations.
- 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 \( g = 10 \, \text{m/s}^2 \))
- 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?
- 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 30Β° to the horizontal. What is the acceleration of the block?
Questions Asked in JEE Advanced exam
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
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Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
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- 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 ________.
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.
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Concepts Used:
Friction
Friction is defined as the resistance offered by the surfaces that are in contact when they move past each other.
Types of Friction
There are four categories of Friction- static friction, sliding friction, rolling friction, and fluid friction.
Sliding Friction
In Sliding Friction, the weight of the sliding object calculates the amount of sliding friction present between the two objects. The sliding friction is supposed to be greater as the pressure exerted by the heavy object on the surface it slides over is comparably more.
Rolling Friction
Friction between a circular object and the surface is called as Rolling Friction. It is required to overcome sliding friction is more than the force required to overcome the rolling friction.
Static Friction
Friction that keeps an object at rest without initiating any relative motion between the body and the surface is termed as Static Friction. For example, a parked car resting on the hill, a hanging towel on the rack. The maximum force of static friction is directly proportional to the normal force.
Fluid Friction
Fluid Friction is the kind of friction that is exerted by the fluid on the object that is moving through a fluid.