CBSE Questions for Class 11 Engineering Physics Motion In A Plane Quiz 10 - MCQExams.com

If $$\overrightarrow A  = 3\widehat i + 2\widehat j\;and\;\overrightarrow B  = 7\widehat i + 24\widehat j,$$ find a vector having the same magnitude as $$\overrightarrow B $$ and parallel to $$\overrightarrow A $$.
  • $$9\widehat i + 6\widehat j$$
  • $$6\widehat i + 10\widehat j$$
  • $$15\widehat i + 20\widehat j$$
  • None of these
For a particle in uniform circular motion, the acceleration a at a point $$P(R,9)$$ on the circle of radius $$R$$ is (Here 0 is measured from the x- axis)
  • $$\frac { v ^ { 2 } } { R } \hat { i } + \frac { v ^ { 2 } } { R } \hat { j }$$
  • $$- \frac { v ^ { 2 } } { R } \cos \theta \hat { i } + \frac { v ^ { 2 } } { 2R } \sin \theta \hat { j }$$
  • $$- \frac { v ^ { 2 } } {2 R } \cos \theta \hat { i } + \frac { v ^ { 2 } } { R } \sin \theta \hat { j }$$
  • $$- \frac { v ^ { 2 } } { R } \cos \theta \hat { i } - \frac {2 v ^ { 2 } } { R } \sin \theta \hat { j }$$
A ring takes time $${t}_{1}$$ in slipping down an inclined plane of length $$L$$ and takes time $${t}_{2}$$ in rolling down the same plane. The ratio $$\frac{{t}_{1}}{{t}_{2}}$$ is
  • $$\sqrt{2}:1$$
  • $$1:\sqrt{2}$$
  • $$1:2$$
  • $$2:1$$
An object moving in a circular path at constant speed has constant 
  • Energy
  • Velocity
  • Acceleration
  • Displacement
There are m points on a straight line $$AB$$ and $$n$$ points on the line $$AC$$ none of them being the point $$A$$. Triangles are formed with these points as vertices, when:
(i) $$A$$ is excluded.
(ii) $$A$$ is included. The ratio of number of triangles in the two
cases is:
  • $$\dfrac { m + n - 2 } { m + n }$$
  • $$\dfrac { m + n - 1 } { m + n  }$$
  • $$\dfrac { m + n - 2 } { m + n + 2 }$$
  • $$\dfrac { m ( n - 1 ) } { ( m + 1 ) ( n + 1 ) }$$
A force of $$ 2\overset { \wedge  }{ i } +3\overset { \wedge  }{ j } +4\overset { \wedge  }{ k }  $$ acts on a body for 4 seconds and produces a displacement  of $$3\overset { \wedge  }{ i } +4\overset { \wedge  }{ j } +5\overset { \wedge  }{ k } m.$$ The power used is 
  • 9.5 W
  • 7 W
  • 6.5 W
  • 4.5 W
The component of a vector is 
  • always less than its magnitude
  • always greater than its magnitude
  • always equal to its magnitude
  • none of these
A particle moves in the xy plane with velocity $${u}_{x}=8t-2$$ and $${u}_{y}=2$$. If it passes through the point $$x=14$$ and $$y=4$$ at $$t=2s$$, the equation of the path is
  • $$x={y}^{2}-y+2$$
  • $$x={y}^{2}-2$$
  • $$x={y}^{2}+y-6$$
  • None of these
A particle moves with constant speed $$v$$ along a circular path of radius $$r$$ and completes the circle in time $$T$$. The acceleration of the particle is
  • $$2\pi v/T$$
  • $$2\pi r/T$$
  • $$2\pi {r}^{2}/T$$
  • $$2\pi {v}^{2}/T$$
A  rigid body rotates about a fixed axis with variable angular velocity equal to $$\alpha  - \beta t$$, at the time $$t$$, where $$\alpha $$,$$\beta $$ are constants. The angular through which it rotates before its stops
  • $$\frac{{{\alpha ^2}}}{{2\beta }}$$
  • $$\frac{{{\alpha ^2} - {\beta ^2}}}{{2\alpha }}$$
  • $$\frac{{{\alpha ^2} - {\beta ^2}}}{{2\beta }}$$
  • $$\frac{{\left( {\alpha - \beta } \right)\alpha }}{2}$$
If $$\vec a,\vec b, \vec c$$ are three coplanar vectors, then $$v\left[ 2\vec { a } +3\vec { b } ,2\vec { b- } 5\vec { c } ,2\vec { c } +3\vec { a }  \right]$$ is 
  • $$0$$
  • $$1$$
  • $$-\sqrt 3$$
  • $$\sqrt 3$$
If $$u,\ v,\ w$$ are non-coplanar vector and $$p,\ q$$ are real numbers, then the equality $$[3u\ pv\ pw]-[pv\ w\ qw]-[2w\ qv\ qu]=0$$ holds for 
  • Exactly two values of $$(p,\ q)$$
  • More than but not all values of $$(p,\ q)$$
  • All values of $$(p,\ q)$$
  • Exactly one values of $$(p,\ q)$$
A body moves in a circle covers equal distance in equal intervals of time. Which of the following remains constant
  • Velocity
  • Acceleration
  • Speed
  • Displacement
Which of the following statements best describes an object undergoing uniforms circular motion?
  • The velocity and acceleration vectors are always tangential to each other
  • Objects in uniform circular motion tend to stay in uniform circular motion
  • The object moves with a constant velocity
  • The object would travel in a straight line if the acceleration vector goes to zero
The equation of a projectile is $$y=ax-b{x}^{2}$$. Its horizontal range is
  • $$\cfrac{a}{b}$$
  • $$\cfrac{b}{a}$$
  • $$a+b$$
  • $$b-a$$
A ball is thrown horizontally from the top of a tower with an initial velocity of 20 meters per second, what is the horizontal velocity of the ball as it hits the ground ?
  • 9.81 m/s
  • 34.3 m/s
  • 20.0 m/s
  • 68.6 m/s
A vector of magnitude 10 has its rectangular component as as 8 and 6 along x axis and y axis respectively. Find the angles it make with the x and y axis?
  • $$ 36.87^o with\  x -axis, 53.13^o with y -axis $$
  • $$ 53.14^o with\  x-axis, 36.86^o $$ with y -axis
  • $$ 47.16^o with\  x- axis 23.92^o with y - axis $$
  • $$ 23.92^o with\  x-axis, 47.16^o with y-axis $$
The path of projectile in the absence of air drag is shown in the figure by dotted line. If the air resistance is not ignored then which one of the path shown in the figure is appropriate for the projectile
1293601_96215bc5a49e40c4a344b32d5fd33295.png
  • B
  • A
  • D
  • C
A ball of mass 0.1 kg is whirled in a horizontal circle of radius 1m, by means of a string at an initial speed of 10 R.P.M. Keeping the radius constant,the tension in the string is reduced to one quarter of its initial value. the new speed is
  • 5 r.p.m
  • 10 r.p.m
  • 20 r.p.m
  • 14 r.p.m
A ball is projected vertically down with an initial velocity from a height of $$15$$ m on to a horizontal floor. During the impact it loses $$25$$% of its energy and rebounds to the same height, the initial velocity of its projections is 
  • $$20\,m{s^{ - 1}}$$
  • $$15\,m{s^{ - 1}}$$
  • $$10\,m{s^{ - 1}}$$
  • $$5\,m{s^{ - 1}}$$
Abody projected up with certain velocity along an inclined plane of coefficient of friction $$0.6$$and slope $$\frac{3}{4}$$ travels for 't' seconds and comes to rest Its time of decent from that position is
  • $$t$$
  • $$9t$$
  • $$3t$$
  • $$5t$$
The length of the second hand of a clock is $$4\ cm$$ the speed of the tip of the second hand is:
  • $$0.24\ cm/s$$
  • $$0.32\ cm/s$$
  • $$0.42\ cm/s$$
  • $$0.50\ cm/s$$
A body is projected with a velocity $$50m{s}^{-1}$$. Distance traveled in 6th second is 
($$g=10m{s}^{-2}$$)
  • $$5m$$
  • $$10m$$
  • $$15m$$
  • $$20m$$
A particle is projected from ground with initial speed $$u$$ at angle $$\theta$$ with horizontal. If air friction is absent, then the average velocity of complete motion will be:
  • $$u\cos{\theta}$$
  • $$u\sin{\theta}$$
  • $$2u\cos{\theta}$$
  • $$2u\sin{\theta}$$
If the vectors $$\bar { AB } =3\hat { i } +4\hat { k } $$ and $$\bar { AC } =5\hat { i } -2\hat j+4\hat k$$ are the sides of a triangle ABC, then the length of the median through A is:
  • $$\sqrt { 18 } $$
  • $$\sqrt { 72 } $$
  • $$\sqrt { 33 } $$
  • $$\sqrt { 45 } $$
The maximum range of a gun or horizontal range is 16 km. If g = 10 $${ ms }^{ -1 }$$. The muzzle velocity of the shell must be:-
  • $$1600 \mathrm { ms } ^ { - 1 }$$
  • $$400 \mathrm { ms } ^ { - 1 }$$
  • $$200 \sqrt { 2 } \mathrm { ms } ^ { - 1 }$$
  • $$160 \sqrt { 10 } \mathrm { ms } ^ { - 1 }$$
A body rotates at $$300$$ rotation per minute. The value in radian of the angle described in $$1$$ sec is
  • $$5$$
  • $$5\pi$$
  • $$10$$
  • $$10 \pi$$
A projectile is projected with a kinetic energy $$K$$. If it has the maximum possible horizontal range, then its kinetic energy at the highest point will be
  • $$K/4$$
  • $$K/2$$
  • $$3K/4$$
  • $$K$$
The potential gradient is a_______
  • vector quantity
  • scalar quantity
  • conversion factor
  • constant
If a particle of mass $$m$$ is moving in a horizontal circle of radius $$r$$ with a centripetal force $$( - \frac{k}{{{r^2}}})$$, the total energy is
  • $$ - \frac{3k}{{2r}}$$
  • $$ - \frac{k}{r}$$
  • $$ - \frac{{2k}}{r}$$
  • $$ - \frac{{4k}}{r}$$
For a particle in uniform circular motion:
  • both velocity and acceleration are constant
  • acceleration and speed are constant but velocity changes
  • both acceleration and velocity changes
  •  Speed is constant
Two particles having position vectors $$\vec { r } = ( 3 \vec { i } + 5 j ) m$$ and $$\vec { r } _ { 2 } = ( - 5 i + 3 j ) m$$ are moving with velocities $$\vec { V } _ { 1 } = ( 4 \hat { i } - 4 \hat { j } ) m s ^ { - 1 }$$ and $$\vec { V } _ { 2 } = ( a \hat { i } - 3 \hat { j } ) m s ^ { - 1 }$$ . If they collide after $$2$$ seconds , the value of $$ a $$ is
  • -$$2$$
  • -$$4$$
  • -$$6$$
  • -$$8$$
Physical quantities are mainly classified into
  • scalars
  • vectors
  • scalars and vectors
  • scalars, vectors and tensors
Which of the following is not a vector quantity
  • speed
  • velocity
  • torque
  • displacement
Time of flights for a particle thrown for equal range at different angles are $$4 s$$ and $$3 s$$. Speed of projection is
  • $$10 m/s$$
  • $$20 m/s$$
  • $$25 m/s$$
  • $$50 m/s$$
A particle move in a circle of radius 5 cm with constant speed and time period 0.2 $$\pi$$s . The acceleration of the particle is :
  • 15 $$m/s^2$$
  • 25 $$m/s^2$$
  • 36 $$m/s^2$$
  • 5 $$m/s^2$$
Position of a particle in a rectangular co - or dinate system is (3 , 2, 5,).Then its position vector will be
  • $$3 \hat i + 5 \hat j + 2 \hat k$$
  • $$3 \hat i + 2 \hat j + 5 \hat k$$
  • $$5 \hat i + 3 \hat j + 2 \hat k$$
  • None of these
The position vector of a particle is determined by the expression $$\vec { r } = 3 t ^ { 2 } \hat { i } + 4 t ^ { 2 } \hat { j } + 7 \hat { k }$$ , The distance traversed in first $$10$$ sec is
  • $$500 m$$
  • $$300 m$$
  • $$150 m$$
  • $$100 m$$
A particle moves along a semicircle of radius $$10\ m$$ in $$5$$ seconds. The average velocity of the particle is 
  • $$2\pi\ ms^{-1}$$
  • $$4\pi\ ms^{-1}$$
  • $$2\ ms^{-1}$$
  • $$4\ ms^{-1}$$
A mass m rotates in a vertical circle, of radius R and has a circular speed $$v_{c}$$ at the top, . If the radius of the circle is increased by a factor of 4, circular speed at the top will be.
  • decreased by a factor of 2
  • decreased by a factor of 4
  • increased by a factor of 2
  • increased by a factor of 4
A cricket player throws a ball at an angle of $$ 53^o $$ with the horizontal.What is the velocity of the projection of the ball if it is caught at the same level by a fielder after 2 seconds?  $$ [take g  = 10 m/s^2 ] $$ 
  • $$6.25 m/s$$
  • $$25 m/s$$
  • $$17.5 m/s$$
  • $$3.53 m/s$$
If two vectors $$\vec { { A }_{ 1 } } =\hat { i } -3\hat { i } +5\hat { k } $$ and $$\vec { { A }_{ 2 } } =\hat { i } -3\hat { j } +a\hat { k } $$ are equal, then the value of a is:
  • +5
  • -5
  • -3
  • 2
A vector $$\vec{A}$$ has magnitude A and $$\hat{A}$$ is unit vector in the direction of $$\vec{A}$$, then which of the following are correct
  • $$\vec{A}. \hat{A} = A$$
  • $$\hat{A} = \dfrac{\vec{A}}{A}$$
  • $$\vec{A}. \vec{A} = A^2$$
  • All of the above
In case of uniform circular motion which of the following physical quantity do not remain constant
  • A.Speed
  • B. Momentum
  • C.Kinetic energy
  • D.Mass
A stone is thrown vertically upward with an initial velocity $$V_0$$. The distance traveled in time $$4v_0 / 3g$$ is
  • $$\dfrac{2v_0^2}{g}$$
  • $$\dfrac{v_0^2}{2g}$$
  • $$\dfrac{4v_0^2}{9g}$$
  • $$\dfrac{5v_0^2}{9g}$$

A particle is projected with velocity 'u' at an angle $$\theta $$ with an inclined plane of inclination $$\theta <45$$ with the horizontal.The time taken when velocity of projectile becomes parallel to the plane 


1434005_c76079a08c2c43bca1fd655bb6de936b.png
  • $$
    \cfrac { u \sin \theta } { g }
    $$
  • $$
    \cfrac { u \cot \theta } { g }
    $$
  • $$
    \cfrac { 2 u \tan \theta } { g }
    $$
  • $$
    \cfrac { u \tan \theta } { g }
    $$
A particle is projected vertically upward with speed $$u=10m/s$$. During its journey air applies a force of $$-.02{v}^{2}$$ on the particle. What is the maximum height attained by the particle ($$m=2kg$$)?
  • $$5\ln{(2)}$$
  • $$3\ln{(2)}$$
  • $$2\ln{(2)}$$
  • $$10\ln{(2)}$$

Vector $$\overrightarrow {\text{A}} $$  lies in xy plane and makes an angle will positive y direction. The x components of $$\overrightarrow {\text{A}} $$ is 
  • $$A\cos \theta $$
  • $$A\sin \theta $$
  • $$A\tan \theta $$
  • $$A\sec \theta $$
A particle moves so that its position vector is given by $$\overrightarrow { r } =\cos ^{  }{ \omega t } \hat { x } +\sin { \omega t } \hat { y } $$, where $$\omega$$ is a constant. Which of the following is true?
  • Velocity is perpendicular to $$\overrightarrow { r } $$ and acceleration is directed away from the origin
  • Velocity and acceleration both are perpendicular to $$\overrightarrow { r } $$
  • Velocity and acceleration both are parallel to $$\overrightarrow { r } $$
  • Velocity is perpendicular to $$\overrightarrow { r } $$ and acceleration is directed towards the origin
An object of mass $$m$$ moves with constant speed in a circular path of radius $$R$$ under the action of a force constatn magnitude $$F$$. The kinetic energy of object is
  • $$\cfrac{1}{2}FR$$
  • $$FR$$
  • $$2FR$$
  • $$\cfrac{1}{4}FR$$
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