Physics-Section-A
1. Which, of the following, is dimensionless?
1.
\(\small\text{impedance}\times\text{conductance} \)
2.
\(\large\frac{\text{emissive power}}{\text{emissivity}}\)
3.
\(\large\frac{\text{electric field}}{\text{magnetic field}}\)
4.
\(\large\frac{\text{inductance}}{\text{capacitance}}\)
2. The linear velocity of a rotating body is given by , where is the angular velocity and r is the radius vector. The angular velocity of a body, and their radius vector is will be:
1.
2.
3.
4.
3. Three non zero vectors satisfy the relation . Then can be parallel to:
(1)
(2)
(3)
(4)
4. A bullet is fired from a gun at the speed of
\(280~\text{ms}^{-1}\) in the direction
\(30^\circ\) above the horizontal. The maximum height attained by the bullet is:
\(\left(g=9.8~\text{m/s}^{2}, \sin30^{\circ}=0.5\right)\)
1. |
\(3000~\text{m}\) |
2. |
\(2800~\text{m}\) |
3. |
\(2000~\text{m}\) |
4. |
\(1000~\text{m}\) |
5. Two
\(1~\text{kg}\) blocks are connected by a light inextensible string and the system is suspended by a spring of stiffness
\(1000~\text{N/m}.\) Take
\(g=10~\text{m/s}^2.\)
The extension in the spring, in equilibrium, is:
1.
\(1~\text{cm}\)
2.
\(2~\text{cm}\)
3.
\(0.5~\text{cm}\)
4.
\(\sqrt2~\text{cm}\)
6. Which of the following quantity is not a vector quantity?
(1) Tension
(2) Angular momentum
(3) Speed
(4) Linear momentum
7. Dimensions of stress are:
1. \(
{\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]}
\)
2. \( {\left[\mathrm{ML}^0 \mathrm{~T}^{-2}\right]}
\)
3. \( {\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]}
\)
4. \( {\left[\mathrm{MLT}^{-2}\right]}\)
8. A ball is projected with a velocity of \(10\) ms–1 at an angle of \(60^\circ\) with the vertical direction. Its speed at the highest point of its trajectory will be:
1. \(10\) ms–1
2. zero
3. \(5\sqrt3\) ms–1
4. \(5\) ms–1
9. Plane angle and solid angle have:
1. |
both units and dimensions |
2. |
units but no dimensions |
3. |
dimensions but no units |
4. |
no units and no dimensions |
10. At what angle must the two forces (x+y) and (x-y) act so that the resultant may be ?
1.
2.
3.
4.
11. A car is moving along a circular path of radius \(500\) m with a speed of \(30\) m/s. If, at some instant, its speed increases at the rate of \(2\) m/s2, then, at that instant, the magnitude of the resultant acceleration will be:
1. \(4.7\) m/s2
2. \(3.8\) m/s2
3. \(3\) m/s2
4. \(2.7\) m/s2
12. The rope and pulley are ideal and there is no friction anywhere except between the
\(10~\text{kg}\)-block and the horizontal plane, where
\(\mu\) (coefficient of friction)
\(=0.2.\) Take
\(g=10~\text{m/s}^2,\) if required.
If
\(m=1~\text{kg},\) what will be the acceleration of the system?
1. |
\(\large\frac{10}{11}\)\(~\text{m/s}^2\) |
2. |
\(\large\frac{9}{10}\)\(~\text{m/s}^2\) |
3. |
\(\large\frac{9}{11}\)\(~\text{m/s}^2\) |
4. |
zero |
13. A metal wire has mass \((0.4\pm 0.002)~\mathrm{g}\), radius \((0.3\pm 0.001)~\mathrm{mm}\) and length \((5\pm 0.02)~\mathrm{cm}\). The maximum possible percentage error in the measurement of density will nearly be:
1. \(1.4 \%\)
2. \(1.2 \%\)
3. \(1.3 \%\)
4. \(1.6 \%\)
15. A ball is thrown at an angle of
\(60^\circ\) above the horizontal, as shown in the adjacent diagram. The fraction of kinetic energy lost by the ball when it reaches its highest point is:
1. |
\(\large\frac{1}{2}\) |
2. |
\(\large\frac{\sqrt3}{2}\) |
3. |
\(\large\frac{1}{4}\) |
4. |
\(\large\frac{3}{4}\) |
16. The minimum work done by the agent in pulling a small particle of mass
\(m\) from
\(A\) to
\(B\) as shown in the figure is:
1.
\(4mgR\)
2.
\(mgR\)
3.
\(3mgR\)
4.
\(2mgR\)
17. A block of mass \(m\) is moving with initial velocity \(u\) towards a stationary spring of stiffness constant \(k\) attached to the wall as shown in the figure. Maximum compression of the spring is:
(The friction between the block and the surface is negligible).
1. |
\(u\sqrt{\dfrac{m}{k}}\) |
2. |
\(4u\sqrt{\dfrac{m}{k}}\) |
3. |
\(2u\sqrt{\dfrac{m}{k}}\) |
4. |
\(\dfrac12u\sqrt{\dfrac{k}{m}}\) |
18. Given below are two statements:
Assertion (A): |
A projectile moving near the earth's surface undergoes an acceleration equal to \(g\) at all points of its trajectory, air resistance being negligible. |
Reason (R): |
When air resistance is negligible, a projectile is in free-fall under gravity and is under the influence of its own weight. |
1. |
Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. |
Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. |
(A) is True but (R) is False. |
4. |
(A) is False but (R) is True. |
19. Which, of the following quantities, is dimensionally independent of mass?
1. \(\dfrac{\text{Energy}}{\text{Time}}\)
2. \(\dfrac{\text{Energy}}{\text{Momentum}}\)
3. \(\small\text{Force}\times{\text{Time}}\)
4. \(\small\text{Pressure}\times{\text{Time}}\)
20. An Atwood's machine with blocks of masses
\(3\) kg and
\(2\) kg is set up in a laboratory. The string is taut and the blocks start moving at
\(t=0.\)
The work done by tension on the
\(3\) kg block has a magnitude
\(W_1\) while the work done by gravity on the same block has a magnitude
\(W_2,\) since the beginning of motion.
1. |
\(W_1=W_2\) |
2. |
\(W_1>W_2\) |
3. |
\(W_1<W_2\) |
4. |
Any of the above can be true |
21. Given below are two statements:
Assertion (A): |
If two particles move with uniform accelerations in different directions, then their relative velocity changes in direction. |
Reason (R): |
Since the acceleration are in different directions, there is a relative acceleration and hence the relative velocity changes. |
1. |
(A) is True but (R) is False. |
2. |
(A) is False but (R) is True. |
3. |
Both (A) and (R) are True and (R) is the correct explanation of (A). |
4. |
Both (A) and (R) are True but (R) is not the correct explanation of (A). |
22. What is the minimum velocity with which a body of mass \(m\) must enter a vertical loop of radius \(R\) so that it can complete the loop?
1. \(\sqrt{2 g R}\)
2. \(\sqrt{3 g R}\)
3. \(\sqrt{5 g R}\)
4. \(\sqrt{ g R}\)
23. The given graph shows the variation of velocity with displacement. Which of the following graphs correctly represents the variation of acceleration with displacement?
24. Which of the following is not an illustration of Newton's third law?
1. |
Flight of a jet plane |
2. |
A cricket player lowering his hands while catching a cricket ball |
3. |
Walking on the floor |
4. |
Rebounding of a rubber ball |
25. A rope of length \(8\) m and linear density \(0.5\) kg/m is lying lengthwise on a smooth horizontal floor. It is pulled by a force of \(12\) N. The tension at the mid-point of the rope would be:
1. \(12\) N
2. \(8\) N
3. \(6\) N
4. \(4\) N
26. A force of N is applied to an object. How much work is done, in Joules, moving the object from x=1 to x=4 meters?
1.
2. 51 J
3.
4.
27. A ball is released from the top of a building \(180~\text{m}\) high. It takes time \(t\) to reach the ground. With what speed should it be projected down so that it reaches the ground in time \(\frac{5t}{6}\)?
1. \(50~\text{ms}^{-1}\)
2. \(61~\text{ms}^{-1}\)
3. \(11~\text{ms}^{-1}\)
4. \(2~\text{ms}^{-1}\)
28. An insect trapped in a circular groove of radius \(10\) cm moves along the groove steadily and completes \(14\) revolutions in \(100\) s. The angular speed of the insect is: \(\Big(\text{Take }\pi=\frac{22}{7}\Big)\)
1. \(0.22\) rad/s
2. \(0.44\) rad/s
3. \(0.88\) rad/s
4. \(1.76\) rad/s
29. A bullet of mass \(10\) g moving horizontal with a velocity of \(400\) m/s strikes a wood block of mass \(2\) kg which is suspended by light inextensible string of length \(5\) m. As a result, the centre of gravity of the block is found to rise a vertical distance of \(10\) cm. The speed of the bullet after it emerges horizontally from the block will be:
1. |
\(100\) m/s |
2. |
\(80\) m/s |
3. |
\(120\) m/s |
4. |
\(160\) m/s |
30. A body of mass \(1\) kg begins to move under the action of a time-dependent force \(\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) \) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along the \(\mathrm{X}\) and \(\mathrm{Y}\)-axis. What power will be developed by the force at the time (\(t\))?
1. \(\left(2 t^2+4 t^4\right) \) W
2. \(\left(2 t^3+3 t^3\right) \) W
3. \(\left(2 t^3+3 t^5\right)\) W
4. \(\left(2 t^3+3 t^4\right) \) W
31. The dimensions \([MLT^{-2}A^{-2}]\) belong to the:
1. electric permittivity
2. magnetic flux
3. self-inductance
4. magnetic permeability
32. The line
\(AB\) makes a
\(45^\circ\) angle with the
\(x\)-axis, but it moves along the negative
\(y\)-axis with a speed of
\(1~\text{m/s}.\) The velocity, of the intersection
\((C)\) of
\(AB\) with
\(x\)-axis, is:
1. |
\(1~\text{m/s}\) along the positive \(x\)-axis |
2. |
\(1~\text{m/s}\) along the negative \(x\)-axis |
3. |
\(\begin{aligned}\large\frac{1}{\sqrt2} ~\text{m/s}& \\ \end{aligned}\) along the positive \(x\)-axis |
4. |
\(\begin{aligned} \large\frac{1}{\sqrt2}~\text{m/s} & \\ \end{aligned}\) along the negative \(x\)-axis |
33. A ball, thrown vertically upward, is observed to move upward with a speed \(v_1\) at time \(t_1\) and a speed \(v_2,\) downward, at time \(t_2.\)
The acceleration of the ball is (downward):
1. \(\frac{v_2-v_1}{t_2-t_1}\)
2. \(\frac{v_2+v_1}{t_2-t_1}\)
3. \(\frac{v_2-v_1}{t_2+t_1}\)
4. \(\frac{v_2+v_1}{t_2+t_1}\)
34. A girl of mass
\(45~\text{kg}\) stands on a weighing machine
\((A)\) which is placed on top of a second weighing machine
\((B).\) The weighing machines, each weigh
\(5~\text{kg}.\) Assume that the readings of the weighing machines can be seen easily. The readings on
\(A\) and
\(B\) are: (take
\(g=10~\text{m/s}^2,\) if required)
1. |
\(45~\text{kg},~50~\text{kg}\) |
2. |
\(50~\text{kg},~55~\text{kg}\) |
3. |
\(47.5~\text{kg},~52.5~\text{kg}\) |
4. |
\(45~\text{kg},~45~\text{kg}\) |
35. A car is going up a slight slope decelerating at
\(0.1\) m/s
2. It comes to a stop after going for
\(5\) s. What was its initial velocity?
1. |
\(0.02\) m/s |
2. |
\(0.25\) m/s |
3. |
\(0.5\) m/s |
4. |
\(1.0\) m/s |
Physics-Section-B
36. A ball is released with a velocity
\((2 \hat{\imath}+2 \hat{\jmath})~ \text{m/s}\) on the rectangular pool table from the point
\((3, 0)\text{ m.}\) All the collisions of the ball are elastic.
After the
\(4^{\text{th}}\) collision with the edges of the board, the location and velocity of the ball will be:
1. |
\((3,0)\text{ m and} ~(2 \hat{\imath}+2 \hat{\jmath}) ~\text{m/s}\) |
2. |
\((0,2)~ \text{m and} ~(2 \hat{\imath}-2 \hat{\jmath}) ~\text{m/s}\) |
3. |
\((1,0) ~\text{m and} ~(2 \hat{\imath}+2 \hat{\jmath}) ~\text{m/s}\) |
4. |
\((2,2)~\text{m and }(-2 \hat{\imath}-2 \hat{\jmath}) ~\text{m/s}\) |
37. Given below are two statements:
Statement I: |
If two projectiles are projected in different directions, their relative velocity remains constant while they are both in the air. |
Statement II: |
Both projectiles fall freely under gravity and they have the same acceleration. |
1. |
Statement I is incorrect and Statement II is correct. |
2. |
Both Statement I and Statement II are correct. |
3. |
Both Statement I and Statement II are incorrect. |
4. |
Statement I is correct and Statement II is incorrect. |
38. A particle moves uniformly in a circle of radius
\(R\) with a speed
\(v.\) When it covers a semi-circle (for the first time), its average velocity is:
1. |
\(v\) |
2. |
\(\large\frac{v}{2}\) |
3. |
\(\large\frac{v}{\pi}\) |
4. |
\(\large\frac{2v}{\pi}\) |
39. Buses ply between two towns,
\((A,B)\) separated by
\(6~\text{km:}\) those going from
\(A\) towards
\(B\) go at
\(20~\text{km/h}\) while those going from
\(B\) to
\(A\) go at
\(30~\text{km/h}.\) If a passenger were to make a round trip from
\(A\) to
\(B\) and back, without stopping, his average speed will be:
1. |
\(25~\text{km/h}\) |
2. |
\(24~\text{km/h}\) |
3. |
\(27~\text{km/h}\) |
4. |
\(28~\text{km/h}\) |
40. A high velocity projectile just pierces
\(4\) steel plates of identical thickness, setup back-to-back; the projectile being incident normally onto the plates. If the projectile is incident at an angle of
\(60^\circ\) with its original direction, the number of plates required to just stop it will be:
1. |
\(1\) |
2. |
\(2\) |
3. |
\(6\) |
4. |
\(8\) |
41. Time intervals measured by a clock give the following readings:
\(1.25\) s, \(1.24\) s, \(1.27\) s, \(1.21\) s and \(1.28\) s.
What is the percentage relative error of the observations?
1. \(2\)%
2. \(4\)%
3. \(16\)%
4. \(1.6\)%
42. Two blocks of equal masses (
\(M\)) connected by a string are kept on a rough horizontal surface as shown in the figure. The coefficient of friction between the blocks and the surface is
µ.
If
\(0<F_1-F_2<2\mu mg\), then the correct statement is:
1. |
the direction of friction on block A is towards right. |
2. |
the direction of friction on block B may be towards left or right. |
3. |
tension in the string must be zero. |
4. |
friction force on block B must be zero. |
43. The sum and difference of two perpendicular vectors of equal length are:
1. Perpendicular to each other and of equal length
2. Perpendicular to each other and of different lengths
3. Of equal length and have an obtuse angle between them
4. Of equal length and have an acute angle between them
44. The estimate of absolute error in the measurement of time using a clock is \(10^{-2}~\text{s}.\) The time difference, \(t=t_1-t_2,\) between two events is determined by using the clock. The error in \(t\) is:
1. \(10^{-2}~\text{s}\)
2. \(2\times10^{-2}~\text{s}\)
3. \({\large\frac12}\times10^{-2}~\text{s}\)
4. zero
45. A block of mass \(m\), placed on a rough incline (as shown) – is observed to remain at rest. The coefficient of friction is \(\mu\). The net force exerted by the incline on the block equals: (in magnitude)
1. \(mg \cos\theta +\mu mg\cos\theta\)
2. \(mg\cos\theta\sqrt{1+\mu^2}\)
3. \(mg\sin\theta\)
4. \(mg\)
46. When a particle of mass
\(m\) moves uniformly, with a speed
\(v,\) in a circle of radius
\(R,\)
1. |
no net force acts on the particle |
2. |
a centripetal force \(\frac{mv^2}{R}\) must be acting on the particle |
3. |
a centrifugal force \(\frac{mv^2}{R}\) must act on the particle |
4. |
no force is acting on the particle |
47. A force \(2x\widehat i - 3y^2\widehat j\) acts on a particle when it is at the location \((\mathrm{x, y}).\) This force is:
1. |
non-conservative |
2. |
conservative and the potential energy is \((\mathrm{x^2-y^3})\) |
3. |
conservative and the potential energy is \((\mathrm{y^3-x^2})\) |
4. |
conservative, but it cannot have a potential energy |
48. A body is dropped from a height of \(100~\text{m}\). At what height the velocity of the body will be equal to one-half of the velocity when it hits the ground?
1. \(25~\text{m}\)
2. \(55~\text{m}\)
3. \(65~\text{m}\)
4. \(75~\text{m}\)
49. Work done by a force (\(F\)) in displacing a body by dx is given by W=. If the force is given as a function of displacement (\(x\)) by \(F \left(x\right) = \left( x^{2} - 2 x + 1\right) \text{N}\), then work done by the force from \(x=0\) to \(x=3\) m is:
1. \(3\) J
2. \(6\) J
3. \(9\) J
4. \(21\) J
50. River of width \(500~\text{m}\) is flowing at a speed of \(10~\text{m/s}\). A swimmer can swim at a speed of \(10~\text{m/s}\) in still water. If he starts swimming at an angle of \(120^\circ\) with the flow direction, then the distance he travels along the river while crossing the river is:
1. \(250~\text{m}\)
2. \(500\sqrt{3}~\text{m}\)
3. \(\frac{500}{\sqrt{3}}~\text{m}\)
4. \(500~\text{m}\)
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