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293 Questions Start Errorless Test
All Exams Allen Objective Errorless
JEE (Main) 2021 Q26 Errorless 4. 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) 2021 Q27 Errorless 4. 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 $50ms^{-1}$ , the impulse imparted to the gun and velocity of recoil of gun are
A.
$0.4kg ms^{-1}, 0.1ms^{-1}$
B.
$0.2kg ms^{-1}, 0.05ms^{-1}$
C.
$0.2kg ms^{-1}, 0.1ms^{-1}$
D.
$0.4kg ms^{-1}, 0.05ms^{-1}$
JEE (Main) 2021 Q28 Errorless 4. 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)
A.
1:1
B.
$\sqrt{2}:1$
C.
$2:1$
D.
$1:\sqrt{2}$
2021 Q29 Errorless 4. 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 $g = 10 \, m/s^{2}$ ] (JEE (Main) 2021)
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) 2021 Q30 Errorless 4. 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) 2021 Q31 Errorless 4. 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 cm
B.
1.25 cm
C.
125 cm
D.
12.5 cm
JEE (Main) 2021 Q32 Errorless 4. Critical Thinking 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 $g = 10m/s^{2}$ )
A.
$0.25\mathrm{s}$
B.
$0.34s$
C.
$0.2s$
D.
$0.4s$
JEE (Main) 2021 Q33 Errorless 4. 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
NEET 2021 Q34 Errorless 4. Critical Thinking MCQ
A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is $(g = 10m/s^{2})$ nearly
A.
4.2 kg m/s
B.
2.1 kg m/s
C.
1.4 kg m/s
D.
0 kg m/s
NEET 2021 Q35 Errorless 4. Critical Thinking MCQ
A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass ā€˜mā€™ is suspended from the rod at 160 cm mark as shown in the figure. Find the value of ā€˜mā€™ such that the rod is in equilibrium ( $g = 10 \, m/s^{2}$ )
A.
$\frac {1}{3} k g$
B.
$\frac {1}{6} k g$
C.
$\frac {1}{1 2} k g$
D.
$\frac {1}{2} k g$
JEE (Main) 2021 Q36 Errorless 14. 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.
$\frac{F}{m}\cos \theta +\mu_K\left(g - \frac{F}{m}\sin \theta\right)$
JEE (Main) 2021 Q37 Errorless 14. Critical Thinking-Friction MCQ
A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is [The coefficient of static friction, $\mu_{s}$ is 0.4]
A.
$\frac{7}{2} mg$
B.
$5mg$
C.
$\frac{mg}{5}$
D.
0
JEE (Main) 2021 Q38 Errorless 14. Critical Thinking-Friction MCQ
The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a $30^{\circ}$ banked road at maximum possible speed without skidding is ____ $\times 10^{3}$ kg m/s $^{2}$
A.
10.2
B.
7.2
C.
12.4
D.
6.96
NEET 2021 Q39 Errorless 14. Critical Thinking-Friction MCQ
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine ( $g = 10 \, m/s^{2}$ )
A.
8.1 kW
B.
12.3 kW
C.
7.0 kW
D.
10.2 kW
JEE (Main) 2020 Q40 Errorless 4. Critical Thinking MCQ
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 $g = 10ms^{-2}$ and the rope to be massless)
A.
100 N
B.
90 N
C.
75 N
D.
70 N
JEE (Main) 2020 Q41 Errorless 4. Critical Thinking MCQ
A uniformly thick wheel with moment of inertia $I$ and radius $R$ is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses $m_1$ and $m_2(m_1 > m_2)$ are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when $m_1$ descents by a distance $h$ is
A.
$\left[\frac{m_1 + m_2}{(m_1 + m_2)R^2 + I}\right]^{\frac{1}{2}}gh$
B.
$\left[\frac{2(m_1 - m_2)gh}{(m_1 + m_2)R^2 + I}\right]^{\frac{1}{2}}$
C.
$\left[\frac{2(m_1 + m_2)gh}{(m_1 + m_2)R^2 + I}\right]^{\frac{1}{2}}$
D.
$\left[\frac{(m_1 - m_2)}{(m_1 + m_2)R^2 + I}\right]^{\frac{1}{2}}gh$
NEET 2020 Q42 Errorless 4. Critical Thinking MCQ
Two bodies of mass 4kg and 6kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is
A.
$g / 10$
B.
$g$
C.
$g / 2$
D.
$g / 5$
JEE (Main) 2020 Q43 Errorless 14. Critical Thinking-Friction MCQ
An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is $(g=10ms^{-2})$
A.
0.80 m
B.
0.60 m
C.
0.45 m
D.
0.20 m
JEE (Main) 2019 Q44 Errorless 4. Critical Thinking MCQ
A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of $45^{\circ}$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is $(g = 10 \, ms^{-2})$
A.
200 N
B.
100 N
C.
140 N
D.
70 N
JEE (Main) 2019 Q45 Errorless 4. Critical Thinking MCQ
A block of mass $10\mathrm{kg}$ is kept on a rough inclined plane as shown in the figure. A force of $3N$ 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 $g = 10ms^{-2}$ )
A.
$32N$
B.
$25N$
C.
$23N$
D.
$18N$
JEE (Main) 2019 Q46 Errorless 4. Critical Thinking MCQ
A particle of mass m is moving in a straight line with momentum p. Starting at time t=0, a force F=kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is
A.
$2\sqrt{\frac{p}{k}}$
B.
$\sqrt{\frac{2p}{k}}$
C.
$\sqrt{\frac{2k}{p}}$
D.
$2\sqrt{\frac{k}{p}}$
JEE (Main) 2019 Q47 Errorless 4. Critical Thinking MCQ
A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height $(p-h)$ diagram is
A.
B.
C.
D.
JEE (Main) 2019 Q48 Errorless 4. Critical Thinking MCQ
A bullet of mass 20 g has an initial speed of $1ms^{-1}$ , just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of $2.5 \times 10^{-2}N$ , the speed of the bullet after emerging from the other side of the wall is close to
A.
$0.4 ms^{-1}$
B.
$0.1 ms^{-1}$
C.
$0.3 ms^{-1}$
D.
$0.7 ms^{-1}$
JEE (Main) 2019 Q49 Errorless 4. Critical Thinking MCQ
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 $0.70 \, ms^{-1}$ with respect to the man. The speed of the man with respect to the surface is
A.
$0.20 \, ms^{-1}$
B.
$0.14 \, ms^{-1}$
C.
$0.47 \, ms^{-1}$
D.
$0.28 \, ms^{-1}$
JEE (Main) 2019 Q50 Errorless 14. Critical Thinking-Friction MCQ
A block kept on a rough inclined plane, as shown in the figure, remains at rest up to a maximum force 2N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10N. the coefficient of static friction between the block and the plane is [Take $g = 10m / s^2$ ]
A.
$\frac{2}{3}$
B.
$\frac{\sqrt{3}}{2}$
C.
$\frac{\sqrt{3}}{4}$
D.
$\frac{1}{2}$