CBSE Questions for Class 11 Engineering Physics Motion In A Plane Quiz 7 - MCQExams.com

A curved section of a rod is banked for a speed $$v$$. If there is no friction between road and tyres of the car, then:
  • car is more likely to slip at speeds higher than $$v$$ than speeds lower than $$v$$
  • car cannot remain in static equilibrium on the curved section
  • car will not slip when moving with speed $$v$$
  • None of the above
A particle of mass $$M$$ is moving in a horizontal circle of radius $$R$$ with uniform speed $$v$$. When the particle moves from one point to a dramatically opposite point, its
  • Momentum does not change
  • Momentum changes by $$2Mv$$
  • Kinetic energy changes by $$\cfrac { M{ v }^{ 2 } }{ 4 } $$
  • Kinetic energy changes by $$M{ v }^{ 2 }$$
A point moves along a circle with speed $$v=at$$. The total acceleration of the point at a time when it has traced $$\dfrac{1}{8}^{th}$$ of the circumference is
  • $$8a$$
  • $$2a\sqrt { 4+{ \pi }^{ 2 } } $$
  • $$a$$
  • $$\cfrac { a }{ 2 } \sqrt { 4+{ \pi }^{ 2 } } $$
When a ceiling fan is switched off, its angular velocity fall to half while it makes $$ 36 $$ rotations . How many more rotations will be make before coming to rest ? (Assume uniform angular retardations ).
  • $$ 36$$
  • $$ 24 $$
  • $$ 18 $$
  • $$ 12 $$
A particle $$A$$ moves along a circle of radius $$R = 50\ cm$$ so that its radius vector $$r$$ relative to the point $$O$$ (figure) rotates with the constant angular velocity $$\omega = 0.40\ rad/s$$. Then magnitude of the velocity of the particle, and the magnitude of its total acceleration will be
691775_be15d927278c46a292f4a073f6610b24.png
  • $$v = 0.4\ m/s, a = 0.4\ m/s^{2}$$
  • $$v = 0.32\ m/s, a = 0.32\ m/s^{2}$$
  • $$v = 0.32\ m/s, a = 0.4\ m/s^{2}$$
  • $$v = 0.4\ m/s, a = 0.32\ m/s^{2}$$
A cricket ball is thrown over a triangle from one end of a horizontal base falls on the other end of the base after grazing the vertex. If $$\theta_1$$ and $$\theta_2$$ are the base angles of projection, then.
  • $$\tan\theta_1 -\tan\theta_2 =\tan\alpha$$
  • $$\sin\theta_1 +\sin\theta_2 =\sin\alpha$$
  • $$\tan\theta_1 +\tan\theta_2 =\tan\alpha$$
  • $$\cos\theta_1 +\cos\theta_2 =\cos \alpha$$
Consider the motion of a particle described by $$x=a\cos { t } ,y=a\sin { t } $$ and $$z=t$$. The trajectory traced by the particle as a function of time is
  • Helix
  • Circular
  • Elliptical
  • Straight line
The position vectors of A, B are a, 6 respectively. The position vector of C is $$\dfrac {5\bar{a}}{3} -\bar{b}$$. Then 3 
  • C is inside the $$\Delta OAB $$
  • C is outside the $$\Delta OAB $$ but inside the angle OAB
  • C is outside the$$\Delta OAB $$ but inside the angle OBA
  • None of these
A particle is moving in a circle of radius $$r$$ with constant speed $$v$$. The change in velocity in moving from $$P$$ to $$Q$$ is
695206_97e9b6ef7a2b464281619fcfd27902a0.png
  • $$2v\cos 20^{\circ}$$
  • $$2v\sin 20^{\circ}$$
  • $$2v\cos 40^{\circ}$$
  • $$2v\sin 40^{\circ}$$
For which of the following physical quantities, it is necessary to indicate direction along with its magnitude?
  • Speed
  • Path length
  • Displacement
  • Temperature
A particle is going with constant speed along a uniform helical and spiral path separately as shown in figure then
 [Assume that the vertical acceleration of the particle is negligible in case (a)]

764023_f85a4cfd602540fa9af962ca9ac54083.png
  • The velocity of the particle is constant in both cases
  • The magnitude of acceleration of the particle is constant in both cases
  • The magnitude of acceleration is constant in (a) and decreasing in (b)
  • The magnitude of acceleration is decreasing continuously in both the cases
Two particles $$P$$ and $$Q$$ are moving on a circle. At a certain instant of time both the particles are diametrically opposite and $$P$$ has tangential acceleration $$8\ m/s^{2}$$ and centripetal centripetal $$5\ m/s^{2}$$ whereas $$Q$$ has only centripetal acceleration of $$1 m/s^{2}$$. At that instant acceleration (in $$m/s^{2})$$ of $$P$$ with respect to $$Q$$ is:
  • $$14$$
  • $$\sqrt {80}$$
  • $$10$$
  • $$12$$
A small object of mass of $$100\ gm$$ moves in a circular path. At a given instant velocity of the object is $$10\hat {i} m/s$$ and acceleration is $$(20\hat {i} + 10\hat {j})m/s^{2}$$. At this instant of time, rate of change of kinetic energy of the object is:
  • $$200\ kgm^{2}/s^{3}$$
  • $$300\ kgm^{2}/s^{3}$$
  • $$10000\ kgm^{2}/s^{3}$$
  • $$20\ kgm^{2}/s^{3}$$
A vector having magnitude $$30$$ unit makes equal angles with each of $$x,y$$ and $$z$$ axes. The component along each of $$x,y$$ and $$z$$-axis are
  • $$10\sqrt {3}$$
  • $$20\sqrt {3}$$
  • $$30\sqrt {3}$$
  • $$18\sqrt {3}$$
A particle is projected up inclined plane such that its component of velocity along the incline is 10m/s. Time of flight is 2 sec and maximum height above the incline is 5m. Then velocity of projection will be:
  • $$10m/s$$
  • $$10\sqrt{2}m/s$$
  • $$5\sqrt{2}m/s$$
  • None
A wheel is at rest. Its angular velocity increases uniformly and become 80 radians second after 5 seconds. The total angular displacement is: 
  • 800 rad
  • 400 rad
  • 200 rad
  • 100 rad
A particle  is projected at an angle $$\theta$$ from ground with speed $$u(g=10m/s^2)$$, then which of the following is true?
  • If $$u=10m/s$$ and $$\theta = 30^o$$, then time of flight will be 1 sec
  • If $$u=10\sqrt{3}m/s$$ and $$\theta=60^o$$, then time of flight will be 3 sec
  • If $$u=10\sqrt{3}m/s$$ and $$\theta=60^o$$, then after 2 sec velocity becomes perpendicular to initial velocity
  • If $$u=10m/s$$ and $$\theta=30^o$$, then velocity never becomes perpendicular to intial velocity during its flight
A particle is moving along a circle such that it completes one revolution in $$40$$ seconds. In $$2$$ minutes $$20$$ seconds, the ratio $$\cfrac { \left| displacement \right|  }{ distance } $$ is
  • $$0$$
  • $$\cfrac{1}{7}$$
  • $$\cfrac{2}{7}$$
  • $$\cfrac{7}{11}$$
A ball is thrown horizontally with velocity $$30m/s$$ from top of a $$60m$$ high tower, simultaneously, another ball is thrown vertically upward with velocity $$40m/s$$ from the bottom of same tower. The shortest distance between the two balls is $$\left( g=10m/{ s }^{ 2 } \right) $$
  • $$36m$$
  • $$48m$$
  • $$60m$$
  • $$45m$$
A motorboat is racing towards the north at 25 $$kmh^{-1}$$ and the water current in that region is 10 $$kmh^{-1}$$  in the direction of 60$$^{\circ}$$ east of south. The resultant velocity of the boat is:
  • 11 $$kmh^{-1}$$
  • 22 $$kmh^{-1}$$
  • 33 $$kmh^{-1}$$
  • 44 $$kmh^{-1}$$
Which of the following is not a scalar quantity? 
  • Temperature
  • Coefficient of friction
  • Charge
  • Impulse
A bird flies from (-3m,4m,-3m) to (7m,-2 m,-3m) in the xyz- coordinates. The bird's displacement vector is given by
  • (4$$\hat{i}+2\hat{j}-6\hat{k}$$)
  • $$(10\hat{i}-6\hat{j})$$
  • ($$\hat{i}-2\hat{j}$$)
  • $$(10\hat{i}+6\hat{j}-6\hat{k})$$
Which of the following is not a property of a null vector?
  • $$\vec{A}$$ + $$\vec{0}$$ = $$\vec{A}$$
  • $$\lambda$$ $$\vec{0}$$ = $$\vec{0}$$ where $$\lambda$$ is a scalar
  • 0$$\vec{A}$$ = $$\vec{A}$$
  • $$\vec{A}$$ - $$\vec{A}$$ = $$\vec{0}$$
A disc rotating about its axis, from rest it acquires a angular speed $$100rev/s$$ in $$4$$ second. The angle rotated by it during these four seconds (in radian) is
  • $$100\pi$$
  • $$200\pi$$
  • $$300\pi$$
  • $$400\pi$$
The (x,y,z) coordinates of two points A and B are given respectively as (0, 4, -2) and (-2, 8, -4). The displacement vector from A to B is:
  • -2$$\hat{i}$$+4$$\hat{j}$$-2$$\hat{k}$$
  • 2$$\hat{i}$$-4$$\hat{j}$$+2$$\hat{k}$$
  • 2$$\hat{i}$$+4$$\hat{j}$$-2$$\hat{k}$$
  • -2$$\hat{i}$$-4$$\hat{j}$$-2$$\hat{k}$$
The circular motion of a particle with constant speed is
  • periodic and simple harmonic.
  • simple harmonic but not periodic.
  • neither periodic nor simple harmonic.
  • periodic but not simple harmonic.
A car goes around uniform circular track of radius $$R$$ at a uniform speed $$v$$ once in every $$T$$ seconds. The magnitude of the centripetal acceleration is $$a_C$$. If the car now goes uniformly around a larger circular track of radius $$2R$$ and experiences a centripetal acceleration of  magnitude $$8a_c$$, then its time period is 
  • $$2T$$
  • $$3T$$
  • $$T/2$$
  • $$3/2 T$$
Which one of the following statements is true?
  • A scalar quantity is the one that is conserved in a process.
  • A scalar quantity is the one that can never take negative values.
  • A scalar quantity is the one that does not vary from one point to another in space.
  • A scalar quantity has the same value for observers with different orientations of the axes.
The equations of motion of a projectile are given by $$x = 36 \ t $$m and $$2y = 96t - 9.8 t^{2}$$ m. The angle of projection is
  • sin$$^{-1}$$(4/5)
  • sin$$^{-1}$$(3/5)
  • sin$$^{-1}$$(4/3)
  • sin$$^{-1}$$(3/4)
A projectile is thrown with an initial velocity $$(a\hat{i}+b\hat{j})ms^{-1}$$, where $$\hat{i}$$ and $$\hat{j}$$ are the unit vectors along horizontal and vertical directions respectively. If the range of projectile is twice the maximum height reached by it, then
  • $$b=\frac{a}{2}$$
  • $$b=a$$
  • $$b = 2a$$
  • $$b= 4a$$
If a body placed at the origin is acted upon by a force $$\overline{F}=(\hat{i}+\hat{j}+\sqrt2\hat{k})$$, then which of the following statements are correct?
1.Magnitude of $$\overline{F}$$ is $$(2+sqrt2)$$
2.Magnitude of $$\overline {F}$$ is 2
3. $$\overline {F}$$ makes an angle of $$45^0$$ with the Z-axis.
4. $$\overline {F}$$ makes an angle of $$30^0$$ with the Z-axis.
Select the correct answer using the codes given below.
  • 1 and 3
  • 2 and 3
  • 1 and 4
  • 2 and 4
The speed of a projectile at its maximum height is $$\dfrac{\sqrt{3}}{2}$$  times its initial speed. If the range of the projectile is P times the maximum height attained by it, then P equals
  • $$4/3$$
  • $$2$$ $$\sqrt{3}$$
  • $$4$$ $$\sqrt{3}$$
  • $$3/4$$
If a body placed at the origin is acted upon by a force $$\vec{F}$$ = $$(\hat{i} + \hat{j} + \sqrt 2 \hat{k})$$, then the following statements are correct?
Magnitude of $$\vec{F}$$ is $$(2 + \sqrt2)$$.
Magnitude of $$\vec{F}$$ is 2.
$$\vec{F}$$ makes an angle of $$45^0$$ with the Z-axis. 
$$\vec{F}$$ makes an angle of $$30^0$$ with the Z-axis. 
Select the correct answer using the codes given below.
  • 1 and 3
  • 2 and 3
  • 1 and 4
  • 2 and 4
A cyclist starts from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown in figure. If he maintains constant speed of 10 $$ms^{-1}$$, what is his acceleration at point R ? 
940463_8c3589e58a104f1a950707a20a0f6b1d.JPG
  • 10 $$ms^{-2}$$
  • 0.1$$ms^{-2}$$
  • 0.01$$ms^{-2}$$
  • 1$$ms^{-2}$$
A bomb is released by a horizontal flying aeroplane. The trajectory of the bomb is
  • a parabola
  • a straight line
  • a circle
  • a hyperbola
In uniform circular motion:
  • both the angular velocity and the angular momentum vary
  • the velocity varies but the momentum remains constant
  • magnitude of both the velocity and the momentum stay constant
  • the momentum varies but the velocity remains constant
A stone tied to the end of a string 100 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 22 s, then the acceleration of the stone is then
  • 16 $$ms^{-2}$$
  • 4$$ms^{-2}$$
  • 12$$ms^{-2}$$
  • 8$$ms^{-2}$$
The relative velocity of $$B$$ as seen from $$A$$ is
  • $$-8\sqrt { 2 } \hat { i } + 6\sqrt { 2 } \hat { j }$$
  • $$4\sqrt { 2 } \hat { i } + 3\sqrt { 3 } \hat { j }$$
  • $$3\sqrt { 5 } \hat { i } + 2\sqrt { 3 } \hat { j }$$
  • $$3\sqrt { 2 } \hat { i } + 4\sqrt { 3 } \hat { j }$$
The minimum number of vectors having different planes which can be added to give zero resultant is
  • $$2$$
  • $$3$$
  • $$4$$
  • $$5$$
A car is moving on a circular path and takes a turn. If $${R_1}$$ and $${R_2}$$ be the reactions on the inner and outer wheels respectively, then
  • $${R_1} = {R_2}$$
  • $${R_1} < {R_2}$$
  • $${R_1} > {R_2}$$
  • $${R_1} \geqslant {R_2}$$
A cube is placed so that one corner is at the origin and three edges are along the $$x-, y-,$$ and $$z$$-axes of a coordinate system. Use vectors to compute
a.   The angle between the edge along the $$z$$-axis (line ab) and the diagonal from the origin to the opposite corner (line ad).
b.   The angle between line $$ac$$ (the diagonal of a face) and line $$ad$$.
980018_1910b24748fc43e98f9e1bedd95c0525.png
  • a. $$\cos^{-1}\dfrac{1}{\sqrt{2}}$$

    b. $$\cos^{-1}\dfrac{\sqrt{2}}{\sqrt{3}}$$
  • a. $$\cos^{-1}\dfrac{1}{\sqrt{3}}$$

    b. $$\cos^{-1}\dfrac{\sqrt{2}}{\sqrt{3}}$$
  • a. $$\cos^{-1}\dfrac{1}{\sqrt{3}}$$

    b. $$\cos^{-1}\dfrac{\sqrt{3}}{\sqrt{3}}$$
  • a. $$\cos^{-1}\dfrac{2}{\sqrt{3}}$$

    b. $$\cos^{-1}\dfrac{\sqrt{2}}{\sqrt{3}}$$
The components of a vector along the $$x$$- and $$y$$-directions are $$(n +1)$$ and $$1$$, respectively. If the coordinate system is rotated by an angle $$\theta = 60^o$$, then the components change to $$n$$ and $$3$$. The value of $$n$$ is
  • $$2$$
  • $$\,1+ \sqrt{3} $$
  • $$\,1- \sqrt{3} $$
  • $$\,1\pm \sqrt{3} $$
An object moves with constant acceleration $$\vec { a }$$. Which of the following expression is/are also constant?
  • $$\dfrac { d\left| \vec { v } \right| }{ dt }$$
  • $$\left| \dfrac { d\vec { v } }{ dt } \right|$$
  • $$\dfrac { d\left( { v }^{ 2 } \right) }{ dt }$$
  • $$\dfrac { d\left( \vec { v } /\left| \vec { v } \right| \right) }{ dt }$$
A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 seconds. Find the angular acceleration. Find the angle rotated during these four seconds.
  • $$300 \pi$$  radians.
  • $$400 \pi .$$ radians
  • $$250 \pi $$ radians.
  • $$200 \pi$$  radians.
A car moves on a circular road describing equal angles about the centre in equal intervals of time. Which of following statements about the velocity of car are not true?
  • Velocity is constant
  • Magnitude of velocity is constant but the direction changes
  • Both magnitude and direction of velocity change
  • Velocity is directed towards the center of circle
A wheel has moment of inertia $$10^{-2} kg-m^2$$ and is making 10 rps. The torque required to stop it in 5 secs is 
  • 12.56
  • 9.42
  • 6.28
  • 3.14
 A disc rotates through 10 radians in 4 seconds. The disc experienced uniform acceleration. If the disc starts from rest, what is the angular velocity after four seconds? 
  • 2.5 radians/sec
  • 5 radians/sec
  • 7.5 radians/sec
  • 10 radians/sec
A pendulum bob of mass $$m = 80 mg$$, carrying a charge of $$q = 2 \times 10^{-8}C$$, is at rest a horizontal uniform electric field of $$E = 20,000 V/m$$. The tension $$T$$ in the thread of the pendulum and the angle $$\alpha$$ it makes with vertical is (take $$g = 9.8 m/s^2$$)
  • $$\alpha \approx 27^o$$
  • $$T \approx 880 \mu N$$
  • $$T = 8.8 \mu N$$
  • $$\alpha \approx 356o$$
A body rotates about a fixed axis with an angular acceleration of $$1$$ rad/$$sec^2$$. Through what does it rotate during the time in which its angular velocity increases from $$5$$ rad/s to $$15$$ rad/s.
  • 100 rad
  • 200 rad
  • 250 rad
  • 150 rad
The angular velocity of a wheel increases from $$100\ m/s$$ to $$300\ m/s$$ in $$10\ s$$. The revolutions made during that time is:
  • $$600$$
  • $$1500$$
  • $$1000$$
  • $$2000$$
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