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Kinematics-2D

118 Questions Start Errorless Test
All Exams Allen Advance Errorless
Q101 Errorless 12. Centripetal and Centrifugal Force MCQ
Two particles of equal masses are revolving in circular paths of radii $r_1$ and $r_2$ respectively with the same speed. The ratio of their centripetal forces is
A.
$\frac{r_2}{r_1}$
B.
$\sqrt{\frac{r_2}{r_1}}$
C.
$\left(\frac{r_1}{r_2}\right)^2$
D.
$\left(\frac{r_2}{r_1}\right)^2$
Q102 Errorless 12. Centripetal and Centrifugal Force MCQ
A particle of mass m is observed from an inertial frame of reference and is forced to move in a circle of radius r with a uniform speed v. The centrifugal force on it is
A.
$\frac{mv^{2}}{r}$ towards the centre
B.
$\frac{mv^{2}}{r}$ away from the centre
C.
$\frac{mv^{2}}{r}$ along the tangent through the particle
D.
Zero
Q103 Errorless 12. Centripetal and Centrifugal Force MCQ
A bowl, containing water and mercury, is revolved rapidly about a vertical axis, then the liquid which remains outermost is
A.
Water
B.
Mercury
C.
Mercury and water both
D.
None of the above
Q104 Errorless 12. Centripetal and Centrifugal Force MCQ
The tube AB forms a quarter circle in a vertical plane. The particle Pcan move without friction in the tube. P is placed at A and displaced slightly. It will
A.
Always be in contact with the outer wall
B.
Always be in contact with the inner wall
C.
Initially be in contact with the inner wall and later with the outer wall
D.
Initially be in contact with the outer wall and later with the inner wall
Q105 Errorless 12. Centripetal and Centrifugal Force MCQ
A small block of mass 0.1kg moves with uniform speed in a horizontal circular groove of radius 1m. The block takes $\pi$ sec to complete one round. The normal contact force by the side will be
A.
0.25 N
B.
0.4 N
C.
0.56 N
D.
0.1 N
Advance Level Q106 Errorless 12. Centripetal and Centrifugal Force MCQ
A particle of mass $m_{1}$ is fastened to one end of a string and one of $m_{2}$ to the middle point, the other end of the string being fastened to a fixed point on a smooth horizontal table. The particles are then projected, so that the two portions of the string are always in the same straight line and describes horizontal circles. Find the ratio of tensions in the two parts of the string
A.
$\frac{m_{1}}{m_{1}+m_{2}}$
B.
$\frac{m_{1}+m_{2}}{m_{1}}$
C.
$\frac{2m_{1}+m_{2}}{2m_{1}}$
D.
$\frac{2m_{1}}{m_{1}+m_{2}}$
Advance Level Q107 Errorless 12. Centripetal and Centrifugal Force MCQ
A toy cart is tied to the end of an unstretched string of length $a$ . When revolved, thy toy cart moves in a horizontal circle of radius $2a$ with a time period $T$ . Now the toy cart is speeded up until it moves in a horizontal circle of radius $3a$ with a period $T'$ . If Hooke's law holds, then
A.
$T' = T$
B.
$T' = (3/2)T$
C.
$T' = (\sqrt{3}/2)T$
D.
$T' = \sqrt{(3/2)}T$
Advance Level Q108 Errorless 12. Centripetal and Centrifugal Force MCQ
A chain of 125 links is $1.25m$ long and has a mass of $2kg$ . With the ends fastened together it is set rotating at $3000 \text{ rev/min}$ . Find the centripetal force on each link
A.
$3.14N$
B.
$314 N$
C.
$\frac{1}{3.14} N$
D.
$\frac{1}{314} N$
Advance Level Q109 Errorless 12. Centripetal and Centrifugal Force MCQ
Two bodies $A$ and $B$ each of mass $m$ are tied together by a light string. Both bodies are bound to move on a frictionless ring in a vertical plane as shown in figure. Both bodies are released from rest from the positions shown in figure. Just after releasing, the tension in the string will be
A.
2mg
B.
$\frac{mg}{2}$
C.
$\frac{mg}{\sqrt{2}}$
D.
$mg\sqrt{2}$
Advance Level Q110 Errorless 12. Centripetal and Centrifugal Force MCQ
A cylindrical tube of length ā€˜lā€™ radius ā€˜rā€™ is filled by liquid of density p is rotated ( $\omega$ ), horizontally about an axis-through one of its edges. The force at the other end by the liquid is,
A.
$\rho\pi r^{2}\omega^{2}l^{2}$
B.
$\frac{\rho\pi r^{2}\omega^{2}l}{2}$
C.
$\frac{\rho\pi r^{2}\omega^{2}l^{2}}{2}$
D.
None of these
Basic Level Q111 Errorless 13. Skidding of Vehicle on Level Road MCQ
A car moves along a horizontal circular road of radius $r$ with velocity $v$ . The coefficient of friction between the wheels and the road is $\mu$ . Which of the following statements is not true
A.
The car will slip if $v > \sqrt{\mu rg}$
B.
The car will slip if $\mu < \frac{v^2}{rg}$
C.
The car will slip if $r > \frac{v^2}{\mu g}$
D.
The car will slip at a lower speed, along with some acceleration, than if it moves at constant speed
Basic Level Q112 Errorless 14. Bending of Cyclist MCQ
A cyclist riding the bicycle at a speed of $14\sqrt{3}ms^{-1}$ takes a turn around a circular road of radius $20\sqrt{3}m$ without skidding. (Given $g = 9.8ms^{-2}$ ), what is his inclination to the vertical
A.
$30^{\circ}$
B.
$90^{\circ}$
C.
$45^{\circ}$
D.
$60^{\circ}$
Advance Level Q113 Errorless 14. Bending of Cyclist MCQ
A racing car of 1000 kg moves round a banked track at a constant speed of 108 km/hr. Assuming the total reaction at the wheels is normal to the track and the horizontal radius of the track is 100m, calculate the angle of inclination of the track to the horizontal (take $g = 10 \, m/s^{2}$ )
A.
$12^{o}$
B.
$27^{o}$
C.
$42^{o}$
D.
$65^{o}$
Advance Level Q114 Errorless 14. Bending of Cyclist MCQ
In the above question, what is the reaction at the wheels
A.
$13450N$
B.
$26900N$
C.
$6725N$
D.
$40350N$
Advance Level Q115 Errorless 14. Bending of Cyclist MCQ
A car is moving with a speed v on a road inclined at an angle $\theta$ in a circular arc of radius r, the minimum coefficient of friction, so that the car does not slip away
A.
$\frac{v^{2}}{rg} = \mu \tan \theta$
B.
$\mu = v^{2} / rg$
C.
$\frac{v^{2} \cos \theta - rg \sin \theta}{rg \cos \theta + v^{2} \sin \theta}$
D.
$\frac{v^{2} \cos \theta - rg \sin \theta}{rg \cos \theta - v^{2} \sin \theta}$
Basic Level Q116 Errorless 15. Vertical Looping MCQ
A 2kg stone at the end of a string 1m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4m/sec. The tension in the string will be 52 N, when the stone is
A.
At the top of the circle
B.
At the bottom of the circle
C.
Halfway down
D.
None of the above
Advance Level Q117 Errorless 15. Vertical Looping MCQ
A particle of mass M carries a charge +Q. It is attached to a string of length l and is whirled in a vertical circle in electric field $\vec{E}$ directed upwards; what should be the minimum speed of the path the loop
A.
$[(g + QE / M)l]^{1/2}$
B.
$[(g - QE / M)l]^{1/2}$
C.
$[(Mg + QE)l]^{1/2}$
D.
$[(Mg - QE)l]^{1/2}$
Advance Level Q118 Errorless 15. Vertical Looping MCQ
A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is
A.
$\sqrt{u^{2}-2gL}$
B.
$\sqrt{2gL}$
C.
$\sqrt{u^{2}-gl}$
D.
$\sqrt{2(u^{2}-gL)}$