A body of mass $m$ rests on horizontal surface, the coefficient of friction between the body and the surface is $\mu$. if the mass is pulled by a force $P$ as shown in the figure, the limiting friction between body and surface will be:
- $ \mu mg $
- $ \mu \left[ mg+\left( \frac{P}{2} \right) \right] $
- $ \mu \left[ mg-\left( \frac{P}{2} \right) \right] $
- $ \mu \left[ mg-\left( \frac{\sqrt{3}P}{2} \right) \right] $
The Correct Option is C
Solution and Explanation
The free body diagram of the various forces acting on body is shown. $ R $ is the reaction of the surface on mass, $ f_{s} $ is frictional force.
Taking the horizontal and vertical components, we have
$ R=mg-P\,\sin \,30^{\circ }=mg-\frac{P}{2} $
Limiting frictional force is
$ F=\mu R=\mu \left[ mg-\frac{P}{2} \right] $
Top Questions on Motion in a plane
- A ball is thrown vertically upwards with an initial velocity of $ 20 \, \text{m/s} $. How high will the ball rise? (Take $ g = 10 \, \text{m/s}^2 $)
- MHT CET - 2025
- Physics
- Motion in a plane
- If the position of the particle as a function of time \( t \) is \( \vec{r} = 8t \hat{i} + 3t^2 \hat{j} + 3 \hat{k} \, \text{m} \), then the acceleration of the particle is (in \( \text{m/s}^2 \))
- KEAM - 2025
- Physics
- Motion in a plane
- A person travelling on a straight line moves with a uniform velocity \( v_1 \) for a distance \( x \) and with a uniform velocity \( v_2 \) for the next \( \frac{3x}{2} \) distance. The average velocity in this motion is \( \frac{50}{7} \, \text{m/s} \). If \( v_1 \) is 5 m/s, then \( v_2 \) is ___ m/s.
- JEE Main - 2025
- Physics
- Motion in a plane
- A cannon placed on a cliff at a height of 375 m fires a cannonball with a velocity of 100 m/s\(^{-1}\) at an angle of 30° above the horizontal. The horizontal distance between the cannon and the target is:
(Acceleration due to gravity \( g = 10 \) ms\(^{-2}\))- TS EAMCET - 2024
- Physics
- Motion in a plane
- The speed \( v \) of a wave on a string depends on the tension \( F \) in the string and the mass per unit length \( m/L \) of the string. If it is known that [F] = [ML][T]–2, the values of the constants \( a \) and \( b \) in the following equation for the speed of a wave on a string are: \[ v = (\text{constant}) F^a \left( \frac{m}{L} \right)^b \]
- OJEE - 2024
- Physics
- Motion in a plane
Questions Asked in KCET exam
- If the number of terms in the binomial expansion of \((2x + 3)^n\) is 22, then the value of \(n\) is:
- KCET - 2025
- Binomial theorem
- Which of the following statements is/are true about equilibrium?
- KCET - 2025
- Equilibrium
A block of certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block and the floor are 0.4 and 0.25 respectively. A constant horizontal force \( F = 20 \, \text{N} \) acts on it so that the velocity of the block varies with time according to the following graph. The mass of the block is nearly (Take \( g = 10 \, \text{m/s}^2 \)):
- KCET - 2025
- work, energy and power
- A random experiment has five outcomes \(w_1, w_2, w_3, w_4, w_5\). The probabilities of the occurrence of the outcomes \(w_1, w_2, w_4, w_5\) are respectively \( \frac{1}{6}, a, b, \frac{1}{12} \) such that \(12a + 12b - 1 = 0\). Then the probabilities of occurrence of the outcome \(w_3\) is:
- KCET - 2025
- Probability
A wooden block of mass M lies on a rough floor. Another wooden block of the same mass is hanging from the point O through strings as shown in the figure. To achieve equilibrium, the coefficient of static friction between the block on the floor and the floor itself is
- KCET - 2025
- Newtons Laws of Motion
Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration