Test : Electrostatics
- An electron of mass me, initially at rest, moves through a certain distance in a uniform electric field in time t1. A proton of mass mp, also initially at rest, takes time t2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio t2/t1 is equal to (A) 1
(B) \displaystyle {{\left( {\frac{{{{m}_{e}}}}{{{{m}_{p}}}}} \right)}^{{1/2}}}
(C) \displaystyle {{\left( {\frac{{{{m}_{p}}}}{{{{m}_{e}}}}} \right)}^{{1/2}}}
(D) \displaystyle \left( {\frac{{{{m}_{p}}}}{{{{m}_{e}}}}} \right)
- Two small metallic spheres each of mass ‘m’ are suspended together with strings of length ‘l’ and placed together. When a quantum of charge ‘q’ is transferred to each, the strings make an angle of 90° with each other. The value of ‘q’ is
(A) l \displaystyle \sqrt{{\pi {{\varepsilon }_{0}}mg}}
(B) l \displaystyle \sqrt{{2\pi {{\varepsilon }_{0}}mg}}
(C) l \displaystyle \sqrt{{4\pi {{\varepsilon }_{0}}mg}}
(D) l \displaystyle \sqrt{{8\pi {{\varepsilon }_{0}}mg}}
\displaystyle \frac{{{{x}^{2}}}}{{\sqrt{{{{x}^{2}}+1}}}}=y
\displaystyle \overrightarrow{{a\,}}=\frac{{d\overrightarrow{{v\,}}}}{{dt}}={{a}_{x}}\hat{i}+{{a}_{y}}\hat{j}
$latex \displaystyle \overrightarrow{{a\,}}=\frac{{d\overrightarrow{{v\,}}}}{{dt}}={{a}_{x}}\hat{i}+{{a}_{y}}\hat{j}$
The instantaneous acceleration is the ratio of change of the velocity with respect to time.
\displaystyle \overrightarrow{{a\,}}=\frac{{d\overrightarrow{{v\,}}}}{{dt}}={{a}_{x}}\hat{i}+{{a}_{y}}\hat{j}
where ax = \frac{{d{{v}_{x}}}}{{dt}};\,{{a}_{y}}\,=\,\frac{{d{{v}_{y}}}}{{dt}}
A
Q 1. A tecometer is used to find: [AFMC 94]
(a) gravitational force (b) surface tension
(c) magnetic force (d) rotational frequency
Q 2. The effect of an external force on the inter-particle distances of a rigid body is :
(a) maximum (b) minimum
(c) zero (d) sometimes maximum and sometimes minimum
Q 3. There are some steel balls in an iron box. They will behave :
(a) like a non-rigid body, because the material of box and balls is different.
(b) like a non-rigid body, because the balls in the box are not stuck at a point.
(c) like a rigid body, because the box and the balls are rigid bodies.
(d) like a rigid body, as the box and the balls are solids.
Q 4. A particle is moving with a uniform speed in a circular path. Which is a constant quantity for the particle? [UP CPMT 97; MP PMT 87]
(a) velocity (b) acceleration (c) kinetic energy (d) displacement
Q 5. The following quantity is not directly related to rotational motion:
(a) mass (b) moment of inertia (c) angular acceleration (d) torque
Q 6. Equivalent to force in rotational motion is :
(a) moment of force (b) impulse (c) moment of inertia (d) none of these
Q 7. The quantities which corresponds in linear motion to the quantities I, , and in rotatory motion are respectively : [RAS 93]
(a) M,
(b) M, \vec{F}, \vec{v} and \vec{p} (c)
M, \vec{p}, \vec{v} and \vec{F} (d) h, \vec{\tau }, \vec{p} and \vec{\tau }
Q 8. The linear velocity is doubled and the angular velocity is halved for a rotating body. How many times will the centripetal acceleration change ?
(a) One (b) Two (c) Four (d) Eight
Q 9. For a rotating body, the following quantity/quantities are necessary :
(a) angular velocity (b) angular velocity and a couple
(c) angular velocity and angular acceleration (d) moment of inertia and the torque
Q 10. While a body rotates about any axis, the quantity equal for all the particles is : [RAJ PET 2003]
(a) linear velocity (b) angular velocity
(c) linear acceleration (d) linear momentum
Q 1l. The rate of change of angular momentum is called: [RAS 93]
(a) angular velocity (b) force (c) torque (d) linear momentum
Q 12. Two particles of a rigid body of masses m1 and m2 are completing one rotation in paths of radius r1 and r2 respectively in same time. The ratio of their angular velocities is:
[UP PET 2000; CBSE 2000; MNR 95: CBSE PMT 2001]
(a) m1r22 : m2r22 (b) r1 : r2 (c) r2 : r1 (d) 1 : 1
Q 13. A particle is moving with a constant angular velocity about an exterior axis. Its linear velocity will depend upon :
(a) perpendicular distance of the particle form the axis.
(b) the mass of particle.
(c) angular acceleration of the particle.
(d) the linear acceleration of the particle.
Q 14. All the particles of a rigid body in a rotatory motion have :
(a) equal linear and angular velocity.
(b) linear velocity equal, but angular velocity unequal.
(c) equal angular velocity, but unequal linear velocity.
(d) both linear and angular velocities unequal.
Q 15. All the particles of a rigid rotating body move in a circular path when the axis of rotation :
(a) passes through any point in the body.
(b) is situated outside the body.
(c) situated any where.
(d) passes through the centre of mass.
Q 16. When a mass rotates about any axis, the direction of the angular velocity will be :
(a) towards radius. (b) towards the tangent to the orbit.
(c) at an angle of 45° to the plane of rotation.(d) along the direction of axis of rotation.
Q 17. The moment of inertia of a rotating body depends: [AFMC 2002; MP PET 86]
(a) only on the mass of the body. (b) only on the distribution of mass.
(c) only on the position of axis of rotation. (d) all of the above.
Q 18. A body of mass m is rotating with angular velocity to on a circular path of radius r. The centripetal force acting on it is : [MP PET 87]
(a) mw (b) mw/r (c) mrw2 (d) mr2w2
Q 19. On account of the earth rotating about its axis :
(a) the linear velocity of objects at equator is greater than at other places.
(b) the angular velocity of object at equator is more than that of object at poles.
(c) the linear velocity of object at all places at the earth is equal, but angular velocity is different.
(d) at all places the angular velocity and linear velocity are uniform.
Q 20. The length of seconds hand of a watch is 1 cm. The change in the velocity of tip of the hand in 15 seconds will be equal to: [RAJ PMT 94: MP PET 87; CPMT 2003]
(a) zero (b) (p/30Ö2) cm/sec (c) (p/30) cm/sec (d) (p/30) Ö2 cm/sec
Q 21. The wheel of an engine executes 4800 rotations per minute. The value of angular velocity in radian/sec will be : [CBSE PMT 95]
(a) 4800 p (b) 2400 p (c) 160 p (d) 80 p
Q 22. The angular velocity of a seconds hand of a watch in radian/sec will be :
[AFMC PUNE 2000; RAJ PMT 94, 99]
(a) 2 (b) 60 (c) p (d) p/30
Q 23. The angular velocity of minutes hand of a watch in radian per second is : [RAJ PMT 98]
(a) p/30 (b) p/60 (c) p/1800 (d) p/3600
Q 24. The linear velocity in cm/sec of a minutes hands of a watch 6 cms long is :
(a) p/2 (b) p/10 (c) p/300 (d) p/600
Q 25. In a particle system, the ratio of angular and linear acceleration of a particle is:
(a) 1/r (b) 1 (c) r (d) r2
Q 26. A wheel starts rotating at 10 rad/sec and attains the angular velocity of 100 rad/sec in 15 sec. What is the angular acceleration in rad/sec2 ?
(a) 10 (b) 110/15 (c) 100/15 (d) 6
Q 27. A particle, moving along a circular path has equal magnitudes of linear and angular acceleration. The diameter of the path is : (in meters)
(a) 1 (b) p (c) 2 (d) 2 p.
Q 28. A wheel starts rotating from rest and attains an angular velocity of 60 rad/sec in 5 seconds. The total angular displacement in radians will be :
(a) 60 (b) 80 (c) 100 (d) 150
Q 29. A body rotates at 300 rotations per minute. The value in radian of the angle described in 1 sec. is:
(a) 5 (b) 5p (c) 10 (d) 10p
Q 30. The linear and angular acceleration of a particle are 10 m/sec2 and 5 rad/sec2 respectively. It will be at a distance from the axis of rotation :
(a) 50 m (b) 1/2 m (c) 1 m (d) 2 m
Q 31. A particle starts from rest under the effect of an acceleration of 5 rad/sec2. The value of angular displacement in 2 seconds in radian will be ?
(a) 10 (b) 20 (c) 20 p (d) 50
Q 32. Due to failure of electricity a fan executing 10 rotations per sec comes to rest in 10 seconds. The number of rotations executed by it, before it stops, will be:
(a) 10 (b) 20 (c) 50 (d) 100
Q 33. The rotational frequency of a wheel decreases from 1000 cycles/min to 400 cycles/min in 10 seconds. The value of retardation in radian/sec2 will be:
(a) 10 (b) 1 (c) (d)
Q 34. Two objects of masses l kg and 2 kg are moving along concentric circles of radii r1 and r2 respectively.
If their angular velocity is same, the ratio of their centripetal accelerations will be:
(a) 2 r1 : r2 (b) r1 : r2 (c) 4r12 : r2 (d) r12 : 4r22
Q 35. A particle, situated in an object, moves with angular acceleration of 6 rad/sec2 and with 2Ö2 rad/sec angular velocity. If the radius of the circular path is 1 m, its total acceleration in m/ sec2 will be:
(a) 1 (b) 100 (c) 10 (d)
Q 36. A wheel rotates with a uniform acceleration of 2 rad/sec2. If it starts from rest, the number of rotations in the first 10 seconds will be: [MPPMT94]
(a) 8 (b) 16 (c) 24 (d) 32.
Q 37. Which of the following pairs, contains physical quantities having different dimensions? [MP PMT 98]
(a) Angular momentum and Planck constant. (b) Moment of inertia and torque.
(c) Work and torque. (d) Impulse and momentum.
Q 38. In which case use of angular velocity is useful? [AFMC97]
(a) When the body is rotating.
(b) When the body moves in a straight line.
(c) When the body is changing its direction of motion.
(d) None of these.
Q 39. If the equation for the displacement of a particle moving on a circular path is given by q = 2t3 + 0.5, where q is in radians and t in seconds, then the angular velocity of the particle at t = 2 sec, is: (in rad/sec) [AIIMS 98]
(a) 8 (b) 12 (c) 24 (d) 36
Answers
1. | 4 | 2. | 3 | 3. | 2 | 4. | 3 | 5. | 1 | 6. | 1 | 7. | 1 |
8. | 1 | 9. | 1 | 10. | 2 | 11. | 3 | 12. | 4 | 13. | 1 | 14. | 3 |
15. | 2 | 16. | 4 | 17. | 4 | 18. | 3 | 19. | 1 | 20. | 4 | 21 | 3 |
22. | 4 | 23. | 3 | 24. | 3 | 25. | 1 | 26. | 4 | 27. | 3 | 28 | 4 |
29. | 4 | 30. | 4 | 31. | 1 | 32. | 3 | 33. | 4 | 34. | 2 | 35. | 3 |
36. | 2 | 37. | 2 | 38. | 1 | 39. | 3 |
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