LFM Pure and Mechanics

iran-konkur 2013 Q162 Assertion-Reason or Statement-Based Conceptual View

162. The velocity of a 2kg ball changes from $\vec{V}_1 = 10\hat{i} - 8\hat{j}$ to $\vec{V}_2 = 6\hat{i} - 5\hat{j}$ (in SI units) under a constant force. If the time of force application is $\frac{1}{10}$ seconds, the magnitude of the force is how many Newtons?
(1) $10$ (2) $12$ (3) $15$ (4) $20$

iran-konkur 2017 Q164 Assertion-Reason or Statement-Based Conceptual View

164- The magnitude of motion (momentum) of a body with mass 2 kg is $6\,\dfrac{\text{kg}\cdot\text{m}}{\text{s}}$. What is the kinetic energy of the body in joules?
(1) $3$ (2) $6$ (3) $9$ (4) $12$

iran-konkur 2018 Q183 Assertion-Reason or Statement-Based Conceptual View

183. A projectile of mass $m$ with initial speed $V_\circ$ is launched at angle $\alpha$ to the horizontal and reaches the ground after $2t$ seconds. What is the magnitude of the change in momentum of the projectile during the first $t$ seconds of motion? (Neglect air resistance.)
$$2mgt \quad (1) \qquad mgt \quad (2) \qquad \dfrac{mv_\circ}{2} \quad (3) \qquad \dfrac{2mv_\circ}{2} \quad (4)$$
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jee-advanced 2007 Q11 Assertion-Reason or Statement-Based Conceptual View

STATEMENT-1
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. because STATEMENT-2 In an elastic collision, the linear momentum of the system is conserved.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True

jee-main 2002 Q15 Velocity of Centre of Mass View

Two identical particles move towards each other with velocity $2v$ and $v$ respectively. The velocity of centre of mass is
(1) $v$
(2) $v/3$
(3) $v/2$
(4) zero

jee-main 2004 Q8 Continuous Force from Repeated Impacts View

A machine gun fires a bullet of mass 40 g with a velocity $1200 \mathrm {~ms} ^ { - 1 }$. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
(1) one
(2) four
(3) two
(4) three

jee-main 2005 Q20 Collision with Spring System View

The block of mass $M$ moving on the frictionless horizontal surface collides with a spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is
(1) $\sqrt{\mathrm{MK}}\,\mathrm{L}$
(2) $\frac{\mathrm{KL}^2}{2\mathrm{M}}$
(3) zero
(4) $\frac{ML^2}{\mathrm{K}}$

jee-main 2006 Q4 Assertion-Reason or Statement-Based Conceptual View

A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of $45^{\circ}$ with the initial vertical direction is
(1) $Mg(\sqrt{2} - 1)$
(2) $Mg(\sqrt{2} + 1)$
(3) $Mg\sqrt{2}$
(4) $\frac{Mg}{\sqrt{2}}$

jee-main 2006 Q9 Explosion or Breakup – Fragment Velocities or Energies View

A bomb of mass 16 kg at rest explodes into two pieces of masses of 4 kg and 12 kg. The velocity of the 12 kg mass is $4$ ms$^{-1}$. The kinetic energy of the other mass is
(1) 96 J
(2) 144 J
(3) 288 J
(4) 192 J

jee-main 2008 Q6 Perfectly Inelastic Collision – Energy Loss View

A block of mass 0.50 kg is moving with a speed of $2.00 \mathrm{~m/s}$ on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is
(1) 0.16 J
(2) 1.00 J
(3) 0.67 J
(4) 0.34 J

jee-main 2010 Q7 Assertion-Reason or Statement-Based Conceptual View

The figure shows the position-time $(x-t)$ graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is
(1) 0.4 Ns
(2) 0.8 Ns
(3) 1.6 Ns
(4) 0.2 Ns

jee-main 2012 Q3 Mass Accretion – Variable Mass System View

Sand is being dropped on a conveyer belt at the rate of 2 kg per second. The force necessary to keep the belt moving with a constant speed of $3 \mathrm {~ms} ^ { - 1 }$ will be
(1) 12 N
(2) 6 N
(3) zero
(4) 18 N

jee-main 2012 Q5 Collision with Spring System View

Two bodies $A$ and $B$ of mass $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. A third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_{0}$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision it is found that the instantaneous velocities of $A$ and $B$ are same and the compression of the spring is $x_{0}$. The spring constant $k$ will be
(1) $m\frac{v_{0}^{2}}{x_{0}^{2}}$
(2) $m\frac{v_{0}}{2x_{0}}$
(3) $2m\frac{v_{0}}{x_{0}}$
(4) $\frac{2}{3}m\left(\frac{v_{0}}{x_{0}}\right)^{2}$

jee-main 2012 Q6 Elastic Collision – Velocity or Mass Determination View

A moving particle of mass $m$, makes a head on elastic collision with another particle of mass $2m$, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to
(1) $33 \%$
(2) $67 \%$
(3) $90 \%$
(4) $10 \%$

jee-main 2014 Q3 Collision Combined with Friction (Embedding/Momentum then Sliding) View

A bullet of mass 4 g is fired horizontally with a speed of $300 \mathrm{~m}/\mathrm{s}$ into 0.8 kg block of wood at rest on a table. If the coefficient of friction between the block and the table is 0.3, how far will the block slide approximately?
(1) 0.19 m
(2) 0.379 m
(3) 0.569 m
(4) 0.758 m

jee-main 2014 Q5 Perfectly Inelastic Collision – Final Velocity View

Three masses $\mathrm{m}$, $2\mathrm{m}$ and $3\mathrm{m}$ are moving in $\mathrm{x}$-$\mathrm{y}$ plane with speed $3\mathrm{u}$, $2\mathrm{u}$ and $\mathrm{u}$ respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be:
(1) $\frac{u}{12}(\hat{i}+\sqrt{3}\hat{j})$
(2) $\frac{u}{12}(\hat{i}-\sqrt{3}\hat{j})$
(3) $\frac{u}{12}(-\hat{i}+\sqrt{3}\hat{j})$
(4) $\frac{u}{12}(-\hat{i}-\sqrt{3}\hat{j})$

jee-main 2017 Q5 Perfectly Inelastic Collision – Final Velocity View

Two particles $A$ and $B$ of equal mass $M$ are moving with the same speed $v$ as shown in figure. They collide completely inelastic and move as a single particle $C$. The angle $\theta$ that the path of $C$ makes with the $X$-axis is given by-
(1) $\tan \theta = \frac { \sqrt { 3 } - \sqrt { 2 } } { 1 - \sqrt { 2 } }$
(2) $\tan \theta = \frac { 1 - \sqrt { 2 } } { \sqrt { 2 } ( 1 + \sqrt { 3 } ) }$
(3) $\tan \theta = \frac { 1 - \sqrt { 3 } } { 1 + \sqrt { 2 } }$
(4) $\tan \theta = \frac { \sqrt { 3 } + \sqrt { 2 } } { 1 - \sqrt { 2 } }$

jee-main 2019 Q3 Elastic Collision – Velocity or Mass Determination View

A simple pendulum, made of a string of length $l$ and a bob of mass $m$, is released from a small angle $\theta _ { 0 }$. It strikes a block of mass $M$, kept on horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle $\theta _ { 1 }$. Then $M$ is given by:
(1) $m \left( \frac { \theta _ { 0 } - \theta _ { 1 } } { \theta _ { 0 } + \theta _ { 1 } } \right)$
(2) $m \left( \frac { \theta _ { 0 } + \theta _ { 1 } } { \theta _ { 0 } - \theta _ { 1 } } \right)$
(3) $\frac { m } { 2 } \left( \frac { \theta _ { 0 } + \theta _ { 1 } } { \theta _ { 0 } - \theta _ { 1 } } \right)$
(4) $\frac { m } { 2 } \left( \frac { \theta _ { 0 } - \theta _ { 1 } } { \theta _ { 0 } + \theta _ { 1 } } \right)$

jee-main 2019 Q3 Elastic Collision – Velocity or Mass Determination View

Two particles of masses $M$ and 2 M are moving with speeds of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, as shown in the figure. They collide at the origin and after that they move along the indicated directions with speeds $v _ { 1 }$ and $v _ { 2 }$, respectively. The values of $v _ { 1 }$ and $v _ { 2 }$ are, nearly
(1) $6.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $3.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $3.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $12.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $13.02 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $19.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $3.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $6.3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

jee-main 2019 Q4 Explosion or Breakup – Fragment Velocities or Energies View

A man (mass $= 50$ kg) and his son (mass $= 20$ kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70 \text{ m s}^{-1}$ with respect to the man. The speed of the man with respect to the surface is:
(1) $0.20 \text{ m s}^{-1}$
(2) $0.14 \text{ m s}^{-1}$
(3) $0.47 \text{ m s}^{-1}$
(4) $0.28 \text{ m s}^{-1}$

jee-main 2019 Q5 Sequential / Multiple Inelastic Collisions View

Three blocks $\mathrm { A } , \mathrm { B }$ and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, $m$ while C has mass $M$. Block A is given an initial speed $v$ towards B due to which it collides with B perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically . $\frac { 5 } { 6 }$ th of the initial kinetic energy is lost in the whole process. What is the value of $M / m$ ?
(1) 3
(2) 4
(3) 5
(4) 2

jee-main 2020 Q4 Sequential / Multiple Inelastic Collisions View

Blocks of masses $\mathrm { m } , 2 \mathrm {~m} , 4 \mathrm {~m}$ and 8 m are arranged in a line of a frictionless floor. Another block of mass m , moving with speed $v$ along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8 m starts moving the total energy loss is $\mathrm { p } \%$ of the original energy. Value of 'p' is close to:
(1) 77
(2) 94
(3) 37
(4) 87

jee-main 2020 Q22 Assertion-Reason or Statement-Based Conceptual View

A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre?

jee-main 2020 Q22 Elastic Collision – Velocity or Mass Determination View

A body A of mass $m = 0.1 \mathrm {~kg}$ has an initial velocity of $3 \hat { \mathrm { i } } \mathrm { m s } ^ { - 1 }$. It collides elastically with another body B of the same mass which has an initial velocity of $5 \hat { \mathrm { j } } \mathrm { m s } ^ { - 1 }$. After the collision, A moves with a velocity $\vec { v } = 4 ( \hat { \mathrm { i } } + \hat { \mathrm { j } } ) \mathrm { m s } ^ { - 1 }$. The energy of B after the collision is written as $\frac { x } { 10 } \mathrm {~J}$. The value of $x$ is $\_\_\_\_$.

jee-main 2021 Q3 Sequential / Multiple Inelastic Collisions View

Three objects $A , B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A , B$ and $C$ are $m , 2 m$ and $2 m$ respectively. $A$ moves towards $B$ with a speed of $9 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C$. All motions occur along the same straight line. The final speed of $C$ is:
(1) $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $9 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

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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