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629 Questions Start Allen Test
All Exams Allen Objective Errorless
JEE (Main) 2021 Q26 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) 2021 Q27 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 $50ms^{-1}$ , 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 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 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 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 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 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 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 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 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 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 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 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 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
NEET 2020 Q40 Objective Medical entrances' gallery MCQ
Two bodies of masses 4 kg and 6 kg 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.
$g / 2$
B.
$g / 5$
C.
$g / 10$
D.
$g$
NEET 2020 Q41 Objective Medical entrances' gallery MCQ
Calculate the acceleration of the block and trolley system shown in the figure. The coefficient of kinetic friction between the trolley and the surface is 0.05 ( $g = 10 \, m/s^{2}$ , mass of the string is negligible and no other friction exists).
A.
$1.25\mathrm{m / s}^2$
B.
$1.50\mathrm{m / s}^2$
C.
$1.66\mathrm{m / s}^2$
D.
$1.00\mathrm{m / s}^2$
JEE (Main) 2020 Q42 Errorless 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 Q43 Errorless 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 Q44 Errorless 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 Q45 Errorless 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
NEET (Odisha) 2019 Q46 Objective Medical entrances' gallery MCQ
A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck, suddenly moves to the right with an acceleration of a. The pendulum will tilt
A.
to the left and the angle of inclination of the pendulum with the vertical is $\sin^{-1}\left(\frac{g}{a}\right)$
B.
to the left and angle of inclination of the pendulum with the vertical is $\tan^{-1}\left(\frac{a}{g}\right)$
C.
to the left and angle of inclination of the pendulum with the vertical is $\sin^{-1}\left(\frac{a}{g}\right)$
D.
to the left and angle of inclination of the pendulum with the vertical is $\tan^{-1}\left(\frac{g}{a}\right)$
NEET (Odisha) 2019 Q47 Objective Medical entrances' gallery MCQ
A body of mass m is kept on a rough horizontal surface (coefficient of friction = $\mu$ ). Horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given F, where F is
A.
$|F| = mg + \mu mg$
B.
$|F| = \mu mg$
C.
$|F| \leq mg \sqrt{1 + \mu^{2}}$
D.
$|F| = mg$
NEET 2019 Q48 Objective Medical entrances' gallery MCQ
A particle moving with velocity v is acted by three forces shown by the vector triangle PQR. The velocity of the particle will
A.
decrease
B.
remain constant
C.
change according to the smallest force $QR$
D.
increase
AIIMS 2019 Q49 Objective Medical entrances' gallery MCQ
Assertion: A glass ball is dropped on concrete floor can easily get broken compared, if it is dropped on wooden floor. Reason: On concrete floor, glass ball will take less time to come to rest.
A.
If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B.
If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C.
If Assertion is correct but Reason is incorrect.
D.
If Assertion is incorrect but Reason is correct.
AIIMS 2019 Q50 Objective Medical entrances' gallery MCQ
A gun applies a force F on a bullet which is given by $F = (100 - 0.5 \times 10^{5} t)$ N. The bullet emerges out with speed 400 m/s. Then, find out the impulse exerted till force on bullet becomes zero.
A.
0.2 N-s
B.
0.3 N-s
C.
0.1 N-s
D.
0.4 N-s