Newton's Laws of Motion

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A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless), so that they slide down the plane. Then, maximum acceleration down the plane is for (no rolling)

Three identical blocks of masses $m = 2 kg$ are drawn by a force $F = 10.2 N$ with an acceleration of $0.6 ms^{- 2}$ on a frictionless surface, then what is the tension (in N) in the string between the blocks $B$ and $C$ ?

A block of mass $m$ is connected to another block of mass $M$ by a spring (massless) of spring constant $k$ . The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then, a constant force $F$ starts acting on the block of mass $M$ to pull it. Find the force on the block of mass $m$ .

(A)

\frac{m F}{M}

(B)

\frac{( M + m ) F}{m}

(C)

\frac{m F}{( m + M )}

(D)

\frac{M F}{( m + M )}

JEE Main 2020

LEVELJEE Advanced

A small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force $mk v^{2}$ , where $v$ is its speed. The maximum height attained by the ball is

(A)

\frac{1}{k} tan^{- 1} (\frac{k u ^{2}}{2 g})

(B)

\frac{1}{2 k} ln (1 + \frac{k u ^{2}}{g})

(C)

\frac{1}{k} ln (1 + \frac{k u ^{2}}{2 g})

(D)

\frac{1}{2 k} tan^{- 1} (\frac{k u ^{2}}{g})

LEVELJEE Advanced

One end of massless rope, which passes over a massless and frictionless pulley $P$ is tied to a hook $C$ while the other end is free. Maximum tension that the rope can bear is $360 N$ . With what value of maximum safe acceleration (in $ms^{- 2}$ ) can a man of $60 kg$ climb on the rope? [Take $g = 10 m/s^{2}$ ]

JEE Main 2021, 18 March Shift-I

LEVELJEE Main

A bullet of mass $0.1 kg$ is fired on a wooden block to pierce through it, but it stops after moving a distance of $50 cm$ into it. If the velocity of bullet before hitting the wood is $10 m/s$ and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is $x N$ . The value of $x$ to the nearest integer is ......... .

JEE Main 2021, 26 Aug Shift-I

LEVELJEE Main

The initial mass of a rocket is $1000 kg$ . Calculate at what rate the fuel should be burnt, so that the rocket is given an acceleration of $20 ms^{- 1}$ . The gases come out at a relative speed of $500 ms^{- 1}$ with respect to the rocket [Use, $g = 10 m/s^{2}$ ]

(A)

6.0 \times 1 0^{2} kg s^{- 1}

(B)

500 kg s^{- 1}

(C)

10 kg s^{- 1}

(D)

60 kg s^{- 1}

JEE Main 2021, 25 July Shift-II

LEVELJEE Main

A force $F = (40 \hat{i} + 10 \hat{j})$ N acts on a body of mass $5 kg$ . If the body starts from rest its position vector $r$ at time $t = 10 s$ will be

(A)

(100 \hat{i} + 400 \hat{j}) m

(B)

(100 \hat{i} + 100 \hat{j}) m

(C)

(400 \hat{i} + 100 \hat{j}) m

(D)

(400 \hat{i} + 400 \hat{j}) m

JEE Main 2021, 20 July Shift-I

LEVELJEE Main

A steel block of $10 kg$ rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration $0.2 m/s^{2}$ . The normal reaction $R$ by the floor, if mass of the iron cylinders are equal and of $20 kg$ each, is ...... $N$ . [Take, $g = 10 m/s^{2}$ and $μ_{s} = 0.2$ ]

A rocket with a lift-off mass $3.5 \times 1 0^{4}$ kg is blasted upwards with an initial acceleration of $10 ms^{- 2}$ . Then, the initial thrust of the blast is

(A)

3.5 \times 1 0^{5}

(B)

7.0 \times 1 0^{5}

(C)

14.0 \times 1 0^{5}

(D)

1.75 \times 1 0^{5}

JEE Main 2021, 26 Feb Shift-I

LEVELJEE Main

A boy pushes a box of mass $2 kg$ with a force $F = (20 \hat{i} + 10 \hat{j}) N$ on a frictionless surface. If the box was initially at rest, then ......... m is displacement along the X-axis after $10 s$ .

JEE Main 2021, 16 March Shift-II

LEVELJEE Main

A body of mass $2 kg$ moves under a force of $(2 \hat{i} + 3 \hat{j} + 5 \hat{k}) N$ . It starts from rest and was at the origin initially. After $4 s$ , its new coordinates are $(8, b, 20)$ . The value of $b$ is ......... . (Round off to the nearest integer)

LEVELJEE Main

A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$ . If a force $P$ is applied at the free end of the rope, the force exerted by the rope on the block is

(A)

\frac{P m}{M + m}

(B)

\frac{P m}{M - m}

(C)

P

(D)

\frac{P M}{M + m}

LEVELJEE Advanced

Two fixed frictionless inclined plane making the angles $3 0^{\circ}$ and $6 0^{\circ}$ with the vertical are shown in the figure. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$ ?

(A)

4.9 ms^{- 2}

in horizontal direction

(B)

9.8 ms^{- 2}

in vertical direction

(C)

zero

(D)

4.9 ms^{- 2}

in vertical direction

LEVELBoard

A particle of mass $0.3 kg$ is subjected to a force $F = - k x$ with $k = 15 Nm^{- 1}$ . What will be its initial acceleration, if it is released from a point $20 cm$ away from the origin?

(A)

3 ms^{- 2}

(B)

15 ms^{- 2}

(C)

5 ms^{- 2}

(D)

10 ms^{- 2}

JEE Main 2019, 10 April Shift-II

LEVELJEE Main

A bullet of mass $20 g$ has an initial speed of $1 ms^{- 1}$ , just before it starts penetrating a mud wall of thickness $20 cm$ . If the wall offers a mean resistance of $2.5 \times 1 0^{- 2} N$ , the speed of the bullet after emerging from the other side of the wall is close to

(A)

0.3 ms^{- 1}

(B)

0.4 ms^{- 1}

(C)

0.1 ms^{- 1}

(D)

0.7 ms^{- 1}

JEE Main 2019, 10 April Shift-I

LEVELJEE Advanced

A ball is thrown upward with an initial velocity $v_{0}$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $mγ v^{2}$ (where, $m$ is mass of the ball, $v$ is its instantaneous velocity and $γ$ is a constant). Time taken by the ball to rise to its zenith is

(A)

\frac{1}{2 γ g} tan^{- 1} (\frac{2 γ}{g} v_{0})

(B)

\frac{1}{γ g} tan^{- 1} (\frac{γ}{g} v_{0})

(C)

\frac{1}{γ g} sin^{- 1} (\frac{γ}{g} v_{0})

(D)

\frac{1}{γ g} ln (1 + \frac{γ}{g} v_{0})

JEE Main 2021, 27 July Shift-II

LEVELJEE Main

A particle of mass $M$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $F = F_{0} [1 - (\frac{t - T}{T})^{2}]$ where, $F_{0}$ and $T$ are constants. The force acts only for the time interval $2 T$ . The velocity $v$ of the particle after time $2 T$ is

(A)

\frac{2 F _{0} T}{M}

(B)

\frac{F _{0} T}{2 M}

(C)

\frac{4 F _{0} T}{3 M}

(D)

\frac{F _{0} T}{3 M}

LEVELJEE Main

Two masses $m_{1} = 5$ kg and $m_{2} = 4.8$ kg tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift is free to move ? ( $g = 9.8 ms^{- 2}$ )

(A)

0.2 ms^{- 2}

(B)

9.8 ms^{- 2}

(C)

5 ms^{- 2}

(D)

4.8 ms^{- 2}

JEE Main 2021, 27 Aug Shift-II

LEVELJEE Advanced

The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (Use, $g = 10 m/s^{2}$ )

JEE Main 2020, 5 Sep Shift-II

LEVELJEE Advanced

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{d M ( t )}{d t} = b v^{2} (t)$ , where $v (t)$ is its instantaneous velocity. The instantaneous acceleration of the satellite is

(A)

- b v^{3} (t)

(B)

- \frac{b v ^{3}}{M ( t )}

(C)

- \frac{2 b v ^{3}}{M ( t )}

(D)

- \frac{b v ^{3}}{2 M ( t )}

LEVELJEE Main

A machine gun fires a bullet of mass $40 g$ with a velocity $1200 ms^{- 1}$ . 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?

A particle of mass $m$ is at rest at the origin at time $t = 0$ . It is subjected to a force $F (t) = F_{0} e^{- b t}$ in the x-direction. Its speed $v (t)$ is depicted by which of the following curves?

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $49 N$ , when the lift is stationary. If the lift moves downward with an acceleration of $5 ms^{- 2}$ , the reading of the spring balance will be

(A)

24 N

(B)

74 N

(C)

15 N

(D)

49 N

LEVELJEE Main

A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (vertically). If the acceleration of the system is $g /8$ , then the ratio of the masses is

(A)

8 : 1

(B)

9 : 7

(C)

4 : 3

(D)

5 : 3

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless), so that they slide down the plane. Then, maximum acceleration down the plane is for (no rolling)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A force F=(40i^+10j^​) N acts on a body of mass 5 kg. If the body starts from rest its position vector r at time t=10 s will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A rocket with a lift-off mass 3.5×104 kg is blasted upwards with an initial acceleration of 10 ms−2. Then, the initial thrust of the blast is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A particle of mass 0.3 kg is subjected to a force F=−kx with k=15 Nm−1. What will be its initial acceleration, if it is released from a point 20 cm away from the origin?

A force $F = (40 \hat{i} + 10 \hat{j})$ N acts on a body of mass $5 kg$ . If the body starts from rest its position vector $r$ at time $t = 10 s$ will be

A rocket with a lift-off mass $3.5 \times 1 0^{4}$ kg is blasted upwards with an initial acceleration of $10 ms^{- 2}$ . Then, the initial thrust of the blast is

A particle of mass $0.3 kg$ is subjected to a force $F = - k x$ with $k = 15 Nm^{- 1}$ . What will be its initial acceleration, if it is released from a point $20 cm$ away from the origin?