JEE (Main) July 2022
Q76
Errorless
Critical Thinking-friction
MCQ
A block 'A' takes 2s to slide down a frictionless incline of $30^{\circ}$ and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is changed to $45^{\circ}$ , the time taken by the block, to slide down the incline, will be approximately
A.
2.66 s
B.
0.83 s
C.
1.68 s
D.
0.70 s
JEE (Main) 2021
Q77
Allen
JEE Main PYQ
MCQ
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 $F = F_0 \left[ 1 - \left( \frac{t - T}{T} \right)^2 \right]$
Where $F_{0}$ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :
A.
$2F_{0}T/M$
B.
$F_{0}T/2M$
C.
$4F_{0}T/3M$
D.
$F_{0}T/3M$
JEE (Main) 2021
Q78
Allen
JEE Main PYQ
MCQ
A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given $m = 8 \, kg$ , $M = 16 \, kg$ Assume all the surfaces shown in the figure to be frictionless.
A.
$\frac{4}{3} g$
B.
$\frac{6}{5} g$
C.
$\frac{3}{5} g$
D.
$\frac{2}{3} g$
JEE (Main) 2021
Q79
Allen
JEE Main PYQ
Numerical
The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be ____ N. $[g = 10 \, ms^{-2}]$
Correct Answer: 25
Explanation:
Ans. (25)
F.B.D. of the block is shown in the diagram Since block is at rest therefore
f r - m g = 0
$F - N = 0\tag{... (1}$
$f r \leq \mu N\tag{... (2}$
In limiting case
$f r = \mu N = \mu F\tag{... (3}$
Using equation (1) and (3)
$\therefore \mu F = m g$
$\Rightarrow F = \frac {0 . 5 \times 1 0}{0 . 2} = 2 5 N$
F.B.D. of the block is shown in the diagram Since block is at rest therefore
f r - m g = 0
$F - N = 0\tag{... (1}$
$f r \leq \mu N\tag{... (2}$
In limiting case
$f r = \mu N = \mu F\tag{... (3}$
Using equation (1) and (3)
$\therefore \mu F = m g$
$\Rightarrow F = \frac {0 . 5 \times 1 0}{0 . 2} = 2 5 N$
JEE (Main) 2021
Q80
Allen
JEE Main PYQ
Numerical
As shown in the figure, a block of mass $\sqrt{3}$ kg is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3\sqrt{3}}$ . The critical force to be applied on the vertical surface as shown at an angle $60^{\circ}$ with horizontal such that it does not move, will be 3x. The value of x will be
$[g = 10m / s^2;\sin 60^\circ = \frac{\sqrt{3}}{2};\cos 60^\circ = \frac{1}{2} ]$
Correct Answer: 3
Explanation:
Ans. (3)
$F\cos 60^{\circ} = \mu N$ or $\frac{F}{2} = \frac{1}{3\sqrt{3}} N$
...(1)
and $N = \sin 60^{\circ} + \sqrt{3} g$
...(2)
From equation 1) and 2)
${\frac {F}{2}} = {\frac {1}{3 \sqrt {3}}} \left({\frac {F \sqrt {3}}{2}} + \sqrt {3} g\right)$
$\Rightarrow \quad F = g = 1 0 \mathrm{Newton} = 3 x$
So $x = \frac{10}{3} = 3.33$
$F\cos 60^{\circ} = \mu N$ or $\frac{F}{2} = \frac{1}{3\sqrt{3}} N$
...(1)
and $N = \sin 60^{\circ} + \sqrt{3} g$
...(2)
From equation 1) and 2)
${\frac {F}{2}} = {\frac {1}{3 \sqrt {3}}} \left({\frac {F \sqrt {3}}{2}} + \sqrt {3} g\right)$
$\Rightarrow \quad F = g = 1 0 \mathrm{Newton} = 3 x$
So $x = \frac{10}{3} = 3.33$
JEE (Main) 2021
Q81
Allen
JEE Main PYQ
Numerical
A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is ____N. (Round off to the Nearest Integer) [Take $g = 10ms^{-2}$ ]
Correct Answer: 30
Explanation:
Ans. (30)
$N + T = 9 0$
$T = \mu N = 0.5 (9 0 - T)$
$1.5 T = 4 5$
$T = 3 0$
$N + T = 9 0$
$T = \mu N = 0.5 (9 0 - T)$
$1.5 T = 4 5$
$T = 3 0$
JEE (Main) 2021
Q82
Allen
JEE Main PYQ
Numerical
When a body slides down from rest along a smooth inclined plane making an angle of $30^{\circ}$ with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time $\alpha T$ , where is $\alpha$ constant greater than 1. The co-efficient of friction between the body and the rough plane is $\frac{1}{\sqrt{x}}\left(\frac{\alpha^{2}-1}{\alpha^{2}}\right)$ where x = .........
Correct Answer: 3
Explanation:
Ans. (3)
On smooth incline
$a = g \sin 3 0 ^ {\circ}$
By $S = ut + \frac{1}{2} at^{2}$
$S = \frac {1}{2} \frac {g}{2} T ^ {2} = \frac {g}{4} T ^ {2}\tag{... (i}$
On rough incline
$a = g \sin 3 0 ^ {\circ} - \mu g \cos 3 0 ^ {\circ}$
By $S = ut + \frac{1}{2} at^{2}$
$S = \frac {1}{4} g (1 - \sqrt {3} \mu) (\alpha T) ^ {2}\tag{... (ii}$
By (i) and (ii)
$\frac {1}{4} g T ^ {2} = \frac {1}{4} g (1 - \sqrt {3} \mu) \alpha^ {2} T ^ {2}$
$\begin{array}{r l} \Rightarrow & 1 - \sqrt {3} \mu = \frac {1}{\alpha^ {2}} \\ \Rightarrow & \mu = \left(\frac {\alpha^ {2} - 1}{\alpha^ {2}}\right) \cdot \frac {1}{\sqrt {3}} \\ \Rightarrow & x = 3. 0 0 \end{array}$
On smooth incline
$a = g \sin 3 0 ^ {\circ}$
By $S = ut + \frac{1}{2} at^{2}$
$S = \frac {1}{2} \frac {g}{2} T ^ {2} = \frac {g}{4} T ^ {2}\tag{... (i}$
On rough incline
$a = g \sin 3 0 ^ {\circ} - \mu g \cos 3 0 ^ {\circ}$
By $S = ut + \frac{1}{2} at^{2}$
$S = \frac {1}{4} g (1 - \sqrt {3} \mu) (\alpha T) ^ {2}\tag{... (ii}$
By (i) and (ii)
$\frac {1}{4} g T ^ {2} = \frac {1}{4} g (1 - \sqrt {3} \mu) \alpha^ {2} T ^ {2}$
$\begin{array}{r l} \Rightarrow & 1 - \sqrt {3} \mu = \frac {1}{\alpha^ {2}} \\ \Rightarrow & \mu = \left(\frac {\alpha^ {2} - 1}{\alpha^ {2}}\right) \cdot \frac {1}{\sqrt {3}} \\ \Rightarrow & x = 3. 0 0 \end{array}$
JEE (Main) 2021
Q83
Allen
JEE Main PYQ
MCQ
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 $^{2}$ )
A.
0.34 s
B.
0.2 s
C.
0.25 s
D.
0.4 s
JEE (Main) Feb. 2021
Q84
Errorless
Critical Thinking
MCQ
An inclined plane making an angle of $30^{\circ}$ with the horizontal is placed in a uniform horizontal electric field $200\frac{N}{C}$ as shown in the figure. A body of mass 1kg and charge 5mC is allowed to slide down from rest at a height of 1m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom $[g=9.8m/s^{2}, \sin30^{\circ}=\frac{1}{2}; \cos30^{\circ}=\frac{\sqrt{3}}{2}]$
A.
0.92 s
B.
0.46 s
C.
2.3 s
D.
1.3 s
JEE (Main) March 2021
Q85
Errorless
Critical Thinking
MCQ
Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period of pendulum will be
A.
$\sqrt{3}T$
B.
$\frac{T}{\sqrt{3}}$
C.
$\sqrt{\frac{3}{2}}T$
D.
$\sqrt{\frac{2}{3}}T$
JEE (Main) July 2021
Q86
Errorless
Critical Thinking
MCQ
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 $F = F_{0} \left[ 1 - \left( \frac{t - T}{T} \right)^{2} \right]$ Where $F_{0}$ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is
A.
$2F_{0}T/M$
B.
$F_{0}T/2M$
C.
$4F_{0}T/3M$
D.
$F_{0}T/3M$
JEE (Main) July 2021
Q87
Errorless
Critical Thinking
MCQ
A force $\vec{F} = (40\hat{i} + 10\hat{j})N$ acts on a body of mass $5kg$ . If the body starts from rest, its position vector $\vec{r}$ at time $t = 10s$ , 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) July 2021
Q88
Errorless
Critical Thinking
MCQ
A steel block of 10kg 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 $0.2m/s^{2}$ . The normal reaction $R'$ by the floor if mass of the iron cylinders are equal and of 20kg each, is ____ N [Take $g = 10m/s^{2}$ and $\mu_{s} = 0.2$ ]
$a = 0.2m / s^{2}$
$a = 0.2m / s^{2}$
A.
716
B.
686
C.
714
D.
684
JEE (Main) July 2021
Q89
Errorless
Critical Thinking
MCQ
If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be
A.
$100\%$
B.
$200\%$
C.
$300\%$
D.
$400\%$
JEE (Main) July 2021
Q90
Errorless
Critical Thinking
MCQ
A bullet of '4g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of $50 \, ms^{-1}$ , the impulse imparted to the gun and velocity of recoil of gun are
A.
$0.4 \, kg \, ms^{-1}, 0.1 \, ms^{-1}$
B.
$0.2 \, kg \, ms^{-1}, 0.05 \, ms^{-1}$
C.
$0.2 \, kg \, ms^{-1}, 0.1 \, ms^{-1}$
D.
$0.4 \, kg \, ms^{-1}, 0.05 \, ms^{-1}$
JEE (Main) July 2021
Q91
Errorless
Critical Thinking
MCQ
Two billiard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is
ball (a)
ball (b)
ball (a)
ball (b)
A.
1:1
B.
$\sqrt{2}:1$
C.
$2:1$
D.
$1:\sqrt{2}$
JEE (Main) Aug. 2021
Q92
Errorless
Critical Thinking
MCQ
The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that rocket is given an acceleration of $20 \, ms^{-2}$ . The gases come out at a relative speed of $500 \, ms^{-1}$ with respect to the rocket [Use $g = 10 \, m/s^{2}$ ]
A.
$6.0 \times 10^{2} \, kg \, s^{-1}$
B.
$500 \, kg \, s^{-1}$
C.
$10 \, kg \, s^{-1}$
D.
$60 \, kg \, s^{-1}$
JEE (Main) Aug. 2021
Q93
Errorless
Critical Thinking
MCQ
Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to
A.
$\sqrt{\frac{m_p}{m_e}}$
B.
$\sqrt{\frac{m_e}{m_p}}$
C.
$\frac{m_p}{m_e}$
D.
$\left(\frac{m_p}{m_e}\right)^{3/2}$
JEE (Main) Aug. 2021
Q94
Errorless
Critical Thinking
MCQ
Two blocks of masses 3 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi} \times 10^{2} N m^{-2}$ . What is the minimum radius of the wire (take $g = 10 m s^{-2}$ )
A.
$1250~\mathrm{cm}$
B.
$1.25~\mathrm{cm}$
C.
$125~\mathrm{cm}$
D.
$12.5~\mathrm{cm}$
JEE (Main) Aug. 2021
Q95
Errorless
Critical Thinking
MCQ
A block of mass $m$ slides on the wooden wedge, which in turn slides backwards on the horizontal surface. The acceleration of the block with respect to the wedge is (Given $m = 8kg, M = 16kg$ . Assume all the surfaces shown in the figure to be frictionless)
A.
$\frac{4}{3} g$
B.
$\frac{6}{5} g$
C.
$\frac{3}{5} g$
D.
$\frac{2}{3} g$
JEE (Main) Aug. 2021
Q96
Errorless
Critical Thinking
MCQ
The boxes of masses $2\mathrm{kg}$ and $8\mathrm{kg}$ are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass $8\mathrm{kg}$ to strike the ground starting from rest (use $g = 10m / s^2$ )
A.
0.25 s
B.
0.34 s
C.
0.2 s
D.
0.4 s
JEE (Main) Aug. 2021
Q97
Errorless
Critical Thinking
MCQ
Angular momentum of a single particle moving with constant speed along circular path
A.
Changes in magnitude but remains same in the direction
B.
Is zero
C.
Remains same in magnitude and direction
D.
Remains same in magnitude but changes in the direction
JEE (Main) Aug. 2021
Q98
Errorless
Graphical Questions
MCQ
An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2N along a frictionless surface with following surface profile. The correct applied force vs distance graph will be
A.
B.
C.
D.
JEE (Advanced) 2021
Q99
Errorless
JEE Section
MSQ
One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight $\alpha W$ is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of $(2\sqrt{2})W$ . Which of the following statement(s) is(are) correct
A.
The vertical component of reaction force at O does not depend on $\alpha$
B.
The horizontal component of reaction force at O is equal to W for $\alpha = 0.5$
C.
The tension in the rope is 2W for $\alpha = 0.5$
D.
The rope breaks if $\alpha > 1.5$
JEE (Main) March 2021
Q100
Errorless
Critical Thinking-friction
MCQ
A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle $\theta$ as shown in figure. The coefficient of kinetic friction is $\mu_{k}$ . Then, the block's acceleration 'a' is given by (g is acceleration due to gravity)
A.
$-\frac{F}{m}\cos \theta -\mu_{K}\left(g - \frac{F}{m}\sin \theta\right)$
B.
$\frac{F}{m}\cos \theta -\mu_K\left(g - \frac{F}{m}\sin \theta\right)$
C.
$\frac{F}{m}\cos \theta -\mu_K\left(g + \frac{F}{m}\sin \theta\right)$
D.
$\frac{F}{m}\cos \theta +\mu_K\left(g - \frac{F}{m}\sin \theta\right)$