LFM Pure and Mechanics

iran-konkur 2013 Q156 View

156- Three forces $\vec{F}_1$, $\vec{F}_2$, $\vec{F}_3$ make pairwise angles of $120^\circ$ with each other. If the magnitudes of the forces are 5, 10, and 15 newtons respectively, find their resultant. How many newtons is it?
(1) zero (2) $5$ (3) $5\sqrt{3}$ (4) $10$

iran-konkur 2017 Q161 View

161- According to the figure below, a horizontal force $F$ is applied to a body. What is the minimum value of $F$ (in terms of the body's weight) so that the body remains stationary on the inclined surface? ($\sin 53^\circ = 0.8$, $g = 10\dfrac{m}{s^2}$)
[Figure: A block of mass $m$ on an inclined plane at $53^\circ$ with a horizontal force $F$ applied, $\mu_s = 1$]
(1) $\dfrac{1}{2}$ (2) $\dfrac{3}{5}$ (3) $\dfrac{4}{5}$ (4) $1$

iran-konkur 2019 Q161 View

161. A uniform rope of mass $40\,\text{kg}$, as shown in the figure below, rests against a frictionless wall. If the wall exerts a force of $300\,\text{N}$ on the rope, how many newtons does the surface exert horizontally on the rope?
$$\left(g = 10\,\frac{\text{N}}{\text{kg}}\right)$$
[Figure: A rope leaning against a wall at an angle, with the base on a horizontal surface]

[(1)] $400$
[(2)] $500$
[(3)] $600$
[(4)] $250\sqrt{3}$

iran-konkur 2023 Q51 View

51 -- A body with mass $5\,\text{kg}$ is placed on a horizontal surface and the coefficients of static and kinetic friction between the body and the surface are $0.5$ and $0.4$ respectively. If we apply a horizontal force of $26\,\text{N}$ to the body, find the acceleration of the body and the force the body exerts on the surface in SI units. $\left(g = 10\,\dfrac{\text{m}}{\text{s}^2}\right)$

[(1)] $10\sqrt{29}$ and $0.2$
[(2)] $25\sqrt{5}$ and $0.2$
[(3)] $10\sqrt{29}$ and $1.2$
[(4)] $25\sqrt{5}$ and $1.2$

jee-main 2002 Q1 View

Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are
(1) $12 \mathrm{~N} , 6 \mathrm{~N}$
(2) $13 \mathrm{~N} , 5 \mathrm{~N}$
(3) $10 \mathrm{~N} , 8 \mathrm{~N}$
(4) $16 \mathrm{~N} , 2 \mathrm{~N}$

jee-main 2002 Q8 Equilibrium force removal View

When forces $F_1, F_2, F_3$ are acting on a particle of mass $m$ such that $F_2$ and $F_3$ are mutually perpendicular, then the particle remains stationary. If the force $F_1$ is now removed then the acceleration of the particle is
(1) $\mathrm{F}_1 / \mathrm{m}$
(2) $\mathrm{F}_2 \mathrm{~F}_3 / \mathrm{mF}_1$
(3) $\left(F_2 - F_3\right) / m$
(4) $\mathrm{F}_2 / \mathrm{m}$

jee-main 2004 Q10 Energy conservation with friction or dissipative forces View

A block rests on a rough inclined plane making an angle of $30 ^ { \circ }$ with the horizontal. The coefficient of static friction between the block and the plane is 0.8 . If the frictional force on the block is 10 N , the mass of the block (in kg ) is (take $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ )
(1) 2.0
(2) 4.0
(3) 1.6
(4) 2.5

jee-main 2005 Q12 View

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration a to keep the block stationary. Then a is equal to
(1) $g/\tan\alpha$
(2) $g\operatorname{cosec}\alpha$
(3) g
(4) $g\tan\alpha$

jee-main 2006 Q3 View

A body falling from rest under gravity passes a certain point $P$. It was at a distance of 400 m from $P$, $4$ s prior to passing through $P$. If $g = 10$ m/s$^2$, then the height above the point P from where the body began to fall is
(1) 720 m
(2) 900 m
(3) 320 m
(4) 680 m

jee-main 2007 Q113 Magnitude of Vector Expression View

The resultant of two forces P N and 3 N is a force of 7 N . If the direction of 3 N force were reversed, the resultant would be $\sqrt { 19 } \mathrm {~N}$. The value of P is
(1) 5 N
(2) 6 N
(3) 3 N
(4) 4 N

jee-main 2012 Q3 Friction on Curved Surface (Limiting Angle) View

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ so that the insect does not slip is given by
(1) $\cot \alpha = 3$
(2) $\sec \alpha = 3$
(3) $\operatorname{cosec} \alpha = 3$
(4) $\cos \alpha = 3$

jee-main 2012 Q4 Minimum Force to Move or Push a Block on a Horizontal Surface View

A block of weight $W$ rests on a horizontal floor with coefficient of static friction $\mu$. It is desired to make the block move by applying minimum amount of force. The angle $\theta$ from the horizontal at which the force should be applied and magnitude of the force $F$ are respectively.
(1) $\theta = \tan ^ { - 1 } ( \mu ) , F = \frac { \mu W } { \sqrt { 1 + \mu ^ { 2 } } }$
(2) $\theta = \tan ^ { - 1 } \left( \frac { 1 } { \mu } \right) , F = \frac { \mu W } { \sqrt { 1 + \mu ^ { 2 } } }$
(3) $\theta = 0 , F = \mu W$
(4) $\theta = \tan ^ { - 1 } \left( \frac { \mu } { 1 + \mu } \right) , F = \frac { \mu W } { 1 + \mu }$

jee-main 2018 Q3 View

A body of mass 2 kg slides down with an acceleration of $3 \mathrm {~m} / \mathrm { s } ^ { 2 }$ on a rough inclined plane having a slope of $30 ^ { \circ }$ . The external force required to take the same body up the plane with the same acceleration will be: $\left( \mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 } \right)$
(1) 4 N
(2) 14 N
(3) 6 N
(4) 20 N

jee-main 2019 Q3 View

Two forces $P$ and $Q$, of magnitude $2F$ and $3F$, respectively, are at an angle $\theta$ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $\theta$ is:
(1) $120 ^ { \circ }$
(2) $60 ^ { \circ }$
(3) $30 ^ { \circ }$
(4) $90 ^ { \circ }$

jee-main 2019 Q3 View

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of $3 N$ is applied on the block. The coefficient of static friction between the plane and the block is 0.6 . What should be the minimum value of force $P$, such that the block does not move downward? (take $g = 10 \mathrm {~ms} ^ { - 2 }$)
(1) 23 N
(2) 25 N
(3) 18 N
(4) 32 N

jee-main 2020 Q3 View

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45 ^ { \circ }$ with the vertical. Then F equals: (Take $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ and the rope to be massless)
(1) 100 N
(2) 90 N
(3) 70 N
(4) 75 N

jee-main 2021 Q1 View

The resultant of these forces $\overrightarrow{OP}, \overrightarrow{OQ}, \overrightarrow{OR}, \overrightarrow{OS}$ and $\overrightarrow{OT}$ is approximately $\_\_\_\_$ N. [Take $\sqrt{3} = 1.7, \sqrt{2} = 1.4$ Given $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ unit vectors along $x, y$ axis]
(1) $-1.5\hat{\mathrm{i}} - 15.5\hat{\mathrm{j}}$
(2) $9.25\hat{i} + 5\hat{j}$
(3) $3\hat{i} + 15\hat{j}$
(4) $2.5\hat{\mathrm{i}} - 14.5\hat{\mathrm{j}}$

jee-main 2021 Q21 View

Two blocks ($m = 0.5 \mathrm {~kg}$ and $M = 4.5 \mathrm {~kg}$) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $\frac { 3 } { 7 }$. Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is $N$. (Round off to the Nearest Integer) [Take $g$ as $9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$]

jee-main 2024 Q21 View

Two forces $\bar { F } _ { 1 }$ and $\bar { F } _ { 2 }$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec { F } _ { 1 }$ and $\vec { F } _ { 2 }$ is $\cos ^ { - 1 } \left( \frac { 1 } { n } \right)$. The value of $| n |$ is $\_\_\_\_$.

jee-main 2025 Q1 View

Q1. A particle moves in $x - y$ plane under the influence of a force $\vec { F }$ such that its linear momentum is $\overrightarrow { \mathrm { p } } ( \mathrm { t } ) = \hat { i } \cos ( \mathrm { kt } ) - \hat { j } \sin ( \mathrm { kt } )$. If k is constant, the angle between $\overrightarrow { \mathrm { F } }$ and $\overrightarrow { \mathrm { p } }$ will be :
(1) $\frac { \pi } { 4 }$
(2) $\frac { \pi } { 6 }$
(3) $\frac { \pi } { 2 }$
(4) $\frac { \pi } { 3 }$

jee-main 2025 Q3 View

Q3. A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg . The branch pulls the chain by a force equal to (if $g = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ ) :
(1) 100 N
(2) 200 N
(3) 300 N
(4) 150 N

jee-main 2025 Q3 View

Q3. A 1 kg mass is suspended from the ceiling by a rope of length 4 m . A horizontal force ' $F ^ { \prime }$ ' is applied at the mid point of the rope so that the rope makes an angle of $45 ^ { \circ }$ with respect to the vertical axis as shown in figure. The [Figure] magnitude of $F$ is : (Assume that the system is in equilibrium and $g = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ )
(1) 10 N
(2) $\frac { 10 } { \sqrt { 2 } } \mathrm {~N}$
(3) 1 N
(4) $\frac { 1 } { 10 \times \sqrt { 2 } } \mathrm {~N}$

jee-main 2025 Q4 View

Q4. A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $0.1 \mathrm {~ms} ^ { - 2 }$. The action force of the system on the floor is equal to:
(1) 196 N
(2) 291 N
(3) 294 N
(4) 297 N

jee-main 2025 Q8 View

Q8. A small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density $\rho _ { 0 }$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :
(1) $m g \left( 1 - \rho \rho _ { 0 } \right)$
(2) $m g \left( 1 + \frac { \rho } { \rho _ { 0 } } \right)$
(3) $m g \left( \frac { \rho _ { 0 } } { \rho } - 1 \right)$
(4) $m g \left( 1 - \frac { \rho _ { 0 } } { \rho } \right) _ { \nabla }$

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LFM Pure and Mechanics

Indices and Surds 96

Exponential Functions 197

Laws of Logarithms 242

Exponential Equations & Modelling 28

Arithmetic Sequences and Series 363

Geometric Sequences and Series 159

Differentiation from First Principles 45

Tangents, normals and gradients 140

Stationary points and optimisation 505

Applied differentiation 76

Indefinite & Definite Integrals 502

Areas Between Curves 71

Areas by integration 221

Volumes of Revolution 68

Numerical integration 49

Vectors Introduction & 2D 211

Vectors 3D & Lines 524

Travel graphs 14

SUVAT in 2D & Gravity 31

Constant acceleration (SUVAT) 78

Variable acceleration (1D) 55

Variable acceleration (vectors) 32

Forces, equilibrium and resultants 24

Newton's laws and connected particles 21

Pulley systems 6

Motion on a slope 6

Friction 8

Momentum and Collisions 34

Moments 28

Parametric curves and Cartesian conversion 9

Parametric differentiation 13

Parametric integration 6

Projectiles 49