CBSE Questions for Class 11 Engineering Physics Motion In A Plane Quiz 8 - MCQExams.com

If the magnitude of the cross product of two vector is $$\sqrt { 3 } $$ times to the magnitude of their scalar product the angle between two vector will be :
  • $$\pi $$
  • $$\frac { \pi }{ 2 } $$
  • $$\frac { \pi }{ 3 } $$
  • $$\frac { \pi }{ 6 } $$
If a particle is rotating with an angular velocity $$\omega$$ and angular acceleration $$\alpha$$, then ,
  • the particle is slowing down, if the directions of both angular velocity and angular acceleration are shown in the same directions
  • the particle is speeding up, if the directions of both angular velocity and angular acceleration are shown in the same directions
  • the particle is slowing down, if both angular velocity and angular acceleration are shown in the opposite directions
  • the particle is speeding up, if both angular velocity and angular acceleration are shown in the opposite directions
A  plate  rotates  about  a  fixed  perpendicular  axis  such that  the  angle  changes  with  time  as $$\theta = 2t^2$$.  Find  the  angular  acceleration in $$rad/s^2$$ .
  • 16
  • 12
  • 4
  • 0
The rotating rod starts from rest and acquires a rotational speed $$\omega =600 rev/min$$ in $$2$$ seconds with constant angular acceleration. The angular acceleration of rod is?
1019625_77fe9f1834774beb9c910d92f1361075.png
  • $$20 \pi rad/s$$
  • $$10 \pi rad/s$$ 
  • $$30 \pi rad/s$$
  • $$5 \pi rad/s$$ 
The centripetal acceleration of a particle varies inversely with the square of the radius r of the circular path. The KE of this particle varies directly as:
  • r
  • $$r^2$$
  • $$r^-2$$
  • $$r^{-1}$$
If $$\overrightarrow { A } +\overrightarrow { B } $$ is a unit vector along x-axis and $$\overrightarrow { A } =\hat { i } -\hat { j } +\hat { k } $$ then what is  $$\overrightarrow { B } $$?
  • $$\hat { j } +\hat { k } $$
  • $$\hat { j } -\hat { k } $$
  • $$\hat { i } +\hat { j } +\hat { k } $$
  • $$\hat { i } +\hat { j } -\hat { k } $$
In a Rutherford scattering experiment when a projectile of charge $$Z_{1}$$ and mass $$M_{1}$$approaches a target nucleus of charge $$Z_{2}$$ and mass $$M_{2}$$ the distance to closest approached is $$r_{0}$$. The energy of the projectile is
  • directly proportional to $$M_{1} \times M_{2}$$
  • directly proportional to $$Z_{1} Z_{2}$$
  • directly proportional to to $$Z_{1}$$
  • directly proportional to mass $$M_{1}$$

A force has magnitude 20N. Its one rectangular component is 12N, the other rectangular component must be:
  • 8 N
  • 14 N
  • 16 N
  • 32 N
A particles is projected from ground in vertically upward direction such that the distance travelled by it in $$5th$$ and $$8th$$ second are equal. The time of flight of the particle is:
  • $$10\ s$$
  • $$12\ s$$
  • $$13\ s$$
  • $$16\ s$$
The minimum number of vectors of unequal magnitude required to produce a zero resultant is :
  • $$2$$
  • $$3$$
  • $$4$$
  • $$more\ than\ 4$$
The linear and angular acceleration of a particle are $$10\ m/sec^2$$ and $$5\ rad/sec^2$$ respectively, it will be at a distance of ___ m  from the axis of rotation
  • $$50\ m$$
  • $$1/2\ m$$
  • $$1\ m$$
  • $$2\ m$$
A particle starts travelling on a circle with constant tangential acceleration. The angle between velocity vector and acceleration vector, at the moment when particle complete half the circular track, is:
  • $$\tan ^{ -1 }{ (2\pi ) }$$
  • $$\tan ^{ -1 }{ (\pi ) }$$
  • $$\tan ^{ -1 }{ (3\pi ) }$$
  • $$\tan^{-1} (2)$$
The direction of a vector $$\overrightarrow { A\\  } $$ is reversed. Find the value of $$\triangle \overrightarrow { A } $$ and $$\triangle \overrightarrow { \left| A \right|  } $$ ?
  • -$$\overrightarrow { A\\ } $$,0
  • $$2\overrightarrow { A\\ } $$,0
  • $$\frac { \overrightarrow { A } }{ 2 } $$,0
  • $$\overrightarrow { A\\ } $$,0
If s=a$$\sin { \omega t } \hat { i }+b\cos { \omega t } \hat { j }$$, the equation of path of particle is
  • $${ { x }^{ 2 }+y }^{ 2 }=\sqrt { { a }^{ 2 }+{ b }^{ 2 } }$$
  • $$\dfrac { { x }^{ 2 } }{ { b }^{ 2 } } +\dfrac { { y }^{ 2 } }{ { a }^{ 2 } } =1$$
  • $$\dfrac { { x }^{ 2 } }{ { a }^{ 2 } } +\dfrac { { y }^{ 2 } }{ { b }^{ 2 } } =1$$
  • $$none\ of\ these$$
three vectors $$\overrightarrow a ,\overrightarrow b \,{\text{and}}\,\overrightarrow c $$ are such that $$\left| {\overrightarrow a  + \overrightarrow b \, + \,\overrightarrow c } \right| = 0$$ a + b + c = t unit. Maximum value of $${(\overrightarrow a - \overrightarrow b)}{(\overrightarrow b - \overrightarrow c)}$$ is.
  • $$
    \dfrac{{t^2 }}
    {{\sqrt 3 }}
    $$
  • $$
    \dfrac{{\sqrt 3 t^2 }}
    {4}
    $$
  • $$
    \dfrac{{t^2 }}
    {{12\sqrt 3 }}
    $$
  • $$
    \dfrac{{t^2 }}
    {{2\sqrt 3 }}
    $$

 Calculate the angle between two vectors 2F and$$\sqrt 2 \,{\rm{F}}$$  so that the resultant force is $${\rm{F}}\sqrt {10} .$$
  • 120 degrees
  • 90 degrees
  • 60 degrees
  • 45 degrees
A body of mass $$5\ kg$$ under the action of constant force $$\vec F={F}_{x}\hat i+{F}_{y}\hat j$$ has velocity at $$t=0\ s$$ as $$\vec v=(6\hat i-2\hat j)m/s$$ and at $$t=10s$$ as $$\vec v=+6\hat j\ m/s$$. The force $$\vec F$$ is:
  • $$(-3\hat i+4\hat j)N$$
  • $$(-\dfrac {3}{5}\hat i+\dfrac {4}{5}\hat j)N$$
  • $$(3\hat i-4\hat j)N$$
  • $$(\dfrac {3}{5}\hat i-\dfrac {4}{5}\hat j)N$$
A vector $$\vec A$$ when added to the vector $$\vec B = 3 \hat i + 4 \hat j$$ yields a resultant vector that is an in the position y -direction and has magnitude equal that of $$\vec B$$ find the magnitude $$\vec A$$
  • $$\sqrt {10}$$
  • $$10$$
  • $$5$$
  • $$\sqrt {15}$$
A fire extinguishing hose pipe disposes watch at a speed of 10 m/s to put off fire on a building. Assuming safe distance from the building on ground is 5 m, What is the maximum height at which water strikes building?
  • 1.75 m
  • 2.5 m
  • 3.75 m
  • 4.75 m
If $$\vec P+\vec Q=\vec P-\vec Q$$, then
  • $$\vec P+\vec 0$$
  • $$\vec Q+\vec 0$$
  • $$|\vec P|=1$$
  • $$|\vec Q|=1$$
The initial position of an object at rest is given by $$3\hat i-8\hat j$$ it moves with constant acceleration and reaches to the position $$2\hat i+4\hat j$$ after $$4\ s$$. What is its acceleration?
  • $$-\dfrac{ 1 }{ 8 } \hat { i } +\dfrac{ 3 }{ 2 } \hat { j }$$
  • $$2\hat { j } -\dfrac{ 1 }{ 8 } \hat { j }$$
  • $$-\dfrac{ 1 }{ 2 } \hat { i } +8\hat { j }$$
  • $$8\hat { i } -\dfrac{ 3 }{ 2 } \hat { j }$$
A tree trunk of diameter $$20cm$$ lies in the horizontal field. A lazy grasshopper wants to jump over the trunk. Find the minimum takeoff speed of the grasshopper that will suffice. (No air drag)
  • $$1.1m/sec$$
  • $$2.2m/sec$$
  • $$3.3m/sec$$
  • $$4.4m/sec$$

The speed of a projectile at the highest point becomes$$\dfrac{1}{\sqrt{2}}$$ times its initial speed. The horizontal range of the projectile will be
  • $$(a) \frac{u^2}{g}$$
  • $$(b) \frac{u^2}{2g}$$
  • $$(c) \frac{u^2}{3g}$$
  • $$(d) \frac{u^2}{4g}$$
If two particles are moving on same circle with different angular velocities $${\omega}_{1}$$ and $${\omega}_{2}$$ and different time period $${T}_{1}$$ and $${T}_{2}$$, then the time taken by $$2$$ to complete one revolution w.r.t particle 1 is
  • $$T=\cfrac { { T }_{ 1 }{ T }_{ 2 } }{ { T }_{ 2 }-{ T }_{ 1 } } $$
  • $$T=\cfrac { { T }_{ 1 }+{ T }_{ 2 } }{ 2 } $$
  • $$T=\cfrac { { T }_{ 1 }{ T }_{ 2 } }{ { T }_{ 2 }+{ T }_{ 1 } } $$
  • $${T}_{2}-{T}_{1}$$
The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is:
  • $$120^0$$
  • $$135^0$$
  • $$90^0$$
  • $$150^0$$

 A particle is fired horizontally with a velocity $$98m{s^{ - 1}}$$ from the top of a tower 490m high. The time taken by the projectile to hit the ground is:$$:\left( {g = 9.8m/{s^2}} \right)$$
  • 2 s
  • 5 s
  • 10 s
  • 20 s

An object has a displacement from position vector $$ \vec{r_1} = (2\hat{i}+ 3\hat{j} )m$$
to  $$ \vec{r_2} = (4\hat{i}+ 6\hat{j}
)m$$ under a force $$\vec{F}  = (3x^2
\hat{i} + 2y \hat{j} )N,$$ then work done by the force is:
  • $$ 24J$$
  • $$ 33J$$
  • $$  83J$$
  • $$ 45J$$
The horizontal component of a projectile velocity is 2 m/s. The equation of the projectile is $$y = 16 x - (\dfrac{5} {4}) x^2.$$ If $$g = 10 m/s^2,$$ the horizontal range is
  • 16 m
  • 8 m
  • 3.2 m
  • 12.8 m
The $$P.V.'s$$ of the vertices of a $$\triangle ABC$$ are $$\bar {i}+\bar {j}+\bar {k}, 4\bar {i}+\bar {j}+\bar {k}, 4\bar {i}+5\bar {j}+\bar {k}$$. The $$P.V.$$ of the circumcentre of $$\triangle ABC$$ is
  • $$\dfrac{5}{2}\bar {i}+3\bar {j}+\bar {k}$$
  • $$5\bar {i}+\dfrac{3}{2}\bar {j}+\bar {k}$$
  • $$5\bar {i}+3\bar {j}+\dfrac{1}{2}\bar {k}$$
  • $$\bar {i}+\bar {j}+\bar {k}$$
Resultant of which of a following may be equal to zero?
  • 10N, 10 N, 10 N
  • 10N, 10 N, 25 N
  • 10N, 10 N, 35 N
  • None of these
A flywheel is initially rotating at $$20 rad/s$$ and has a constant angular accelerations After $$9.0s$$ it has rotated through $$450rad$$.Its angular acceleration is 
  • $$3.3 rad/s$$
  • $$4.4 rad/s$$
  • $$5.6 rad/s$$
  • $$6.7 rad/s$$
The positive vector of a particle is determined by the expression $$\vec{r} = 3 t^2 \hat{i} + 4t^2 \hat{j} + 7 \hat{k}$$. The distance traversed in first 10 sec is:
  • 500 m
  • 300 m
  • 150 m
  • 100 m
A wheel initially has an angular velocity of $$18rad/s$$.IT has a constant acceleration of $$2.0 rad/s^2$$ and is slowing at first.What time elapses before its angular velocity is $$18rad/s$$ in the direction opposite to its initial angular velocity?
  • $$3.0s$$
  • $$6.0s$$
  • $$9.0s$$
  • $$18s$$
If $$\hat {i},\hat {j},\hat {k}$$ are positive vectors of $$A,B,C$$ and $$\vec {AB}=\vec {CX}$$, then positive vector of $$X$$ is
  • $$-\hat {i}+\hat {j}+\hat {K}$$
  • $$\hat {i}-\hat {j}+\hat {K}$$
  • $$\hat {i}+\hat {j}-\hat {K}$$
  • $$\hat {i}+\hat {j}+\hat {K}$$
A projectile is thrown at an angle of $$60^\circ $$ with the horizontal with an initial speed of 2 m/sec, with H being highest point of its trajectory. Another particle P is now forced to move along its speed is continuously increasing. When the particle P is at H, $$\vert \vec{V}_p\vert = 20 m/sec, \vert \vec{a}_p\vert = 50 m/sec^2$$, then acceleration vector $$\vec a_p$$ at H equals (take $$g = 10 m/s^{2}$$)
1056636_c51bf804277b4260bc90dbf2e1065123.PNG
  • $$50 \hat{i} m/s^2$$
  • $$- 50 \hat{i} m/s^2$$
  • $$(20 \sqrt{6} \hat i - 10 \hat{j}) m/s^2$$
  • $$(30 \hat i - 40 \hat{j}) m/s^2$$
Given in the diagram OB = BA. The time taken to cover OB is $$T_1$$ and the time take to cover BA is $$T_2$$, then the ratio $$T_1 /T_2$$ is
1051482_fafcca306d16464982cf2f5c647fe198.png
  • = 1
  • > 1
  • < 1
  • cannot be determined
A particle is moving on a circular path of $$10 m$$ radius. At any instant of time its speed is $$5 m/s$$ and the speed is increasing at a rate of $$2 m/s^2$$. At this  instant  the magnitude of the  net acceleration will be nearly.
  • $$3.2 m/s^2$$
  • $$2 m/s^2$$
  • $$2.5 m/s^2$$
  • $$4.3 m/s^2$$
The position vector of a particle is given by $$\vec { r } ={ \vec { r }  }_{ 0 }(1-at)t$$, where $$t$$ is the time and $$a$$ as well as $${\vec { r }  }_{ 0 }$$ are constant. After what time the particle returns to the starting point?
  • $$a$$
  • $$\dfrac{1}{a}$$
  • $$A^2$$
  • $$\dfrac{a}{a^2}$$
A wheel starts from the rest and attains an angular velocity of 20 radian/s after being uniformly accelerated for 10 s.The total angle in radian through which it has turned in 10 second is
  • $$20 \pi$$
  • $$40 \pi$$
  • $$100$$
  • $$100 \pi$$
From a point on the ground a particle is projected with initial velocity $$u$$, such that its horizontal range is maximum. The magnitude of average velocity during its ascent.
  • $$\dfrac{\sqrt 5u}{2\sqrt 2}$$
  • $$\dfrac{5u}{4}$$
  • $$\dfrac{\sqrt 3}{2 \sqrt2}$$
  • $$none$$

Two forces $$\widehat {\text{i}}{\text{ + }}\widehat {\text{j}}{\text{ + }}\widehat {\text{k}}\;{\text{N}}\;{\text{and}}\;\widehat {\text{i}}{\text{ + 2}}\widehat {\text{j}}{\text{ + 3}}\widehat {\text{k}}\;{\text{N}}$$ act on a particle and displace it from (2,3,4) to point (5,4,3). Displacement is in m. Work done is: 
  • $$5 J$$
  • $$4 J$$
  • $$3 J$$
  • None of these
A particle is attached at one end of massless rod whose other end is fixed at $$O$$ as shown in figure. A particle is given minimum velocity at lower most point to complete vertical circular motion about $$O$$. Find net force on the particle when it is at position $$P$$. Length of rod is $$\ell$$.
1077563_ca5bcfada2b545379505f08f3f0ab50c.png
  • $$\dfrac{18mg}{5}$$
  • $$\dfrac{23mg}{5}$$
  • $$\dfrac{\sqrt{333}mg}{5}$$
  • $$None\ of\ above$$
The height $$y$$ and horizontal distance $$x$$ covered by a projectile in a time $$t$$ seconds are given by the equations $$y = 8t - 5t^2$$ and $$x = 6t$$. If $$x$$ and $$y$$ are measured in meters, the velocity of projection is:-
  • $$10 \ ms^{-1}$$
  • $$6 \ ms^{-1}$$
  • $$8 \ ms^{-1}$$
  • $$14 \ ms^{-1}$$
A ball is thrown at angle $$\theta$$ and another ball is thrown at an angle $$(90-\theta)$$ with the horizontal direction from the same point with the same speed $$40 ms^{-1}$$. The second ball reaches $$50m$$ higher than the first ball. Find their individual heights.
  • $$20m , 70m$$
  • $$25m , 75m$$
  • $$15m , 65m$$
  • $$10m , 60m$$
For two particles A and B, given that $$\overrightarrow {r}_A = 2\hat{i} + 3\hat{j},$$ $$\overrightarrow{r}_B = 6\hat{i} + 7\hat{j},$$ $$\overrightarrow {V}_A = 3\hat{i} - \hat{j}$$ and $$\overrightarrow{v}_B = x\hat{i} - 5\hat{j}.$$ what is the value of x if they collide.
  • 1
  • 7
  • 2
  • -2
A ball has been thrown vertically up such that distance covered by it in $$4th$$ and $$6th$$ second is same. If $$g=10m/s^2$$, the initial speed of the ball is
  • $$45m/s$$
  • $$25m/s$$
  • $$50m/s$$
  • $$10m/s$$

A body starts rotating from rest and completes 10 revolutions in 4 sec. Find its angular acceleration    
  • $$2.5\pi \,\,{\text{rad/}}{{\text{s}}^{\text{2}}}$$
  • $$5\pi \,\,{\text{rad/}}{{\text{s}}^{\text{2}}}$$
  • $$7.5\pi \,\,{\text{rad/}}{{\text{s}}^{\text{2}}}$$
  • $$10\pi \,\,{\text{rad/}}{{\text{s}}^{\text{2}}}$$
A body is projected vertically upwards with a velocity of $$19.6 \ m/s$$. The total time for which the body will remain in the air is (Take $$g = 9.8 m/s^2$$)
  • $$4 \ s$$
  • $$6 \ s$$
  • $$9 \ s$$
  • $$12 \ s$$
If the direction of cosines of a vector are $$\dfrac{3}{5 \sqrt 2}, \dfrac{4}{5 \sqrt 2}$$ and $$\dfrac{1}{\sqrt 2}$$ respectively, then the vector is:
  • $$3 \hat{i} + 4 \hat{j} + \hat{k}$$
  • $$3 \hat{i} + 4 \hat{j} + \sqrt 5 \hat{k}$$
  • $$3 \sqrt{2} \hat{i} + 4 \sqrt{2} \hat{j} + \hat{k}$$
  • $$3 \hat{i} + 4 \hat{j} + 5 \hat{k}$$
A ball is thrown from a point on ground at some angle of projection. At the time a bird starts from a point directly above this point of projection at a height $$h $$ horizontally with speed $$u$$. Given that in its flight ball just touches the bird at one point. Find the distance on ground where ball strikes:
  • $$2 u \sqrt{\dfrac{h}{g}}$$
  • $$u \sqrt{\dfrac{2h}{g}}$$
  • $$2 u \sqrt{\dfrac{2h}{g}}$$
  • $$ u \sqrt{\dfrac{h}{g}}$$
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