CBSE Questions for Class 11 Engineering Physics Motion In A Plane Quiz 14 - MCQExams.com

The position vector of a particle is given as $$
\vec{r}=\left(t^{2}-4 t+6\right) \hat{i}+\left(t^{2}\right) \hat{\jmath}
 $$. The time atter which the velocity vector and acceleration vector becomes perpendicular to each other is equal to
  • 1sec
  • 2 sec
  • 1.5 sec
  • not possible
A ball is projected vertically down with an initial velocity from a height f $$20m$$ onto a horizontal floor. During the impact it loses $$50$$% of its energy and rebounds to the same height. The initial velocity of its projection is
  • $$20m{s}^{-1}$$
  • $$15m{s}^{-1}$$
  • $$10m{s}^{-1}$$
  • $$5m{s}^{-1}$$
Two particles of equal mass have velocities $$\vec { V }1 = a \hat { j } $$ and   $$ \vec { V } 2 =  a \hat { j } $$. The acceleration of first particle is $$ \vec { a } = b( \hat { i}  + \hat { j} ) $$ where a and b are constant. If the accelaeration of the second particle is zero, the centre of mass of the two particles moves along a 
  • straight line
  • circle
  • ellipse
  • parabola
The range of a projectile is $$48\ m$$. Consider $$x=4$$ to be the point of projection. The x-coordinate of the projectile where the kinetic energy is minimum is
  • 48 m
  • 20 m
  • 24 m
  • 12 m
Find the projection of $$\overrightarrow { a } =2\hat { i } -\hat { j } +\hat { k } $$ on $$\overrightarrow { b } =\hat { i } -2\hat { j } +\hat { k } $$
  • $$\cfrac{5}{\sqrt{6}}$$
  • $$\cfrac{7}{10}$$
  • $$\cfrac{6}{\sqrt{5}}$$
  • $$\cfrac{5}{\sqrt{3}}$$
A child's top is spun with angular accelertion $$\alpha =4t^{3}-3t^{2}+2t$$ where t is in second and $$\alpha $$ is in radians per second square. At t=0 the top has angular velocity $$\omega _{0}=2 rad/s$$ and a reference line on it is at an angular position $$\theta _{0}=1$$
Statement I: Expression for angular velocity $$\omega =\left ( 2+t^{2}+t^{3}+t^{4} \right )rad/s$$
Statement II: Expression for angular positon $$\theta =\left ( 1+2t-3t^{2}+4t^{3} \right )$$
  • Only statement-I is true
  • Only statement II is true
  • Both of them are true
  • None of them are true
The maximum height at which a small mass $$m$$ can be placed on the parabolic bowl without slipping is 
$$(\mu_{s}=0.5.Equation\ of\ parabolic\ bowll\ is\ y=\dfrac {x^{2}}{10}where\ x\ and\ y\ are\ in\ metre)$$
1379955_703523c222764acdbd5261724e422feb.png
  • $$30\ cm$$
  • $$35\ cm$$
  • $$40\ cm$$
  • $$62.5\ cm$$
A block hangs from a string wrapped on a disc of radius $$20 \mathrm{cm}  $$ free to rotate about its axis which is fixed in a horizontal position.If the angular speed of the disc is $$10 \mathrm{rad} / \mathrm{s} $$ at some instant, with what speed is the block going down at that instant?
  • $$4 m / s $$
  • $$3 m / s $$
  • $$2 \mathrm{m} / \mathrm{s} $$
  • $$5 \mathrm{m} / \mathrm{s} $$
Make correct statements.
  • Two particles thrown with same speed from the same point at the same instant but at different angles cannot collide in mid IR.
  • A body projected in uniform gravitational field follows a parabolic path.
  • In projectile motion, velocity is never perpendicular to the acceleration.
  • A particle dropped from rest and blown over by a horizontal wind with constant velocity traces a parabolic path.
A particle is moving with a velocity of $$\bar { v } =\left( 3\hat { i } +4t\hat { j }  \right) m/s$$. Find the ratio of tangential acceleration to that of total acceleration at t=1 sec:
  • $$\dfrac{4}{5}$$
  • $$\dfrac{3}{5}$$
  • $$\dfrac{5}{4}$$
  • $$\dfrac{3}{4}$$
A ball of mass $$0.5\ { kg }$$ is attached to the end of a string having a length $$0.5\ m $$. The ball is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is $$324\ { N }$$. The maximum possible value of the angular velocity of the ball (in radians) is:
  • $$9$$
  • $$18$$
  • $$27$$
  • $$36$$
A $$50 kg$$ girl wearing a high heel shoes balances on a single heel. The heel is circular with a diameter $$1 cm$$ what is the pressure exerted by the heel on the floor?
  • $$(490/785\times 10^{-3})pa$$
  • $$(785\times 10^{-3}/490)pa$$
  • $$(490/7.85\times 10^{-3})pa$$
  • $$(490\times 10^{-4})pa$$
 A park of mass 3m is projected from the ground at some angle with horizontal. The horizontal, range is R. At the highest point of its path, it breaks into two pieces m and 2m. The smaller small mass comes to rest and larger mass finally falls at a distance x from the point of projection where equal to
  • $$

    \frac{3 R}{4}

    $$
  • $$

    \frac{3 R}{2}

    $$
  • $$

    \frac{5 R}{4}

    $$
  • 3R
A particle is projected at an angle of $$60^o$$ above the horizontal with a speed of $$10 \ ms^{-1}$$. After some time the velocity makes an angle of $$30^o$$ above the horizontal. The speed of the particle at this instant is?
  • $$ 5\sqrt3 \ ms^{-1} $$
  • $$ 5\  ms^{-1} $$
  • $$ \dfrac{5}{\sqrt3}ms^{-1} $$
  • $$ \dfrac{10}{\sqrt3}ms^{-1} $$
The position vector of a point lying on the joining the points whose position vectors are $$\overline i + \overline j -\overline k$$ and $$\overline i - \overline j +\overline k$$ is
  • $$\overline j$$
  • $$\overline i$$
  • $$\overline k$$
  • $$\overline 0$$
The position vectors of two particles change with time as $$\underset{r{\rightarrow}}=(t^{2}-3t+4)\hat{i}+(t^{2}-t)$$ and  $$\underset{r_{2}}{\rightarrow}=(2t-2)\hat{i}+t\hat{j}$$ 
Choose correct alternative (s) if $$|\underset{r}{\rightarrow}|$$  and t are in meters and seconds respectively:
  • Particles will collide at t = $$2_{g}$$
  • Particles will collide at t = $$3_{s}$$
  • Particles will collide at t = $$0_{s}$$
  • Particles will collide at t = $$1_{s}$$
A toy projectile of mass  $$m$$  can be separated into two equal masses by a light spring. When the toy projectile is moving horizontally with  $$4 m/s,$$  the spring breaks up the projectile. One part goes vertically downward with a velocity of  $$6 m/s.$$  The speed of the other half of the projectile at that instant will be
  • zero
  • $$2 m/s$$
  • $$\sqrt { 20 } { m }/{ s }$$
  • $$10 m/s$$
In a plitical rally a guy from audience throws at leader. The flower travels is a horizontaly distance of 20 m in 1 s before hitting the leader's face 1.75m above the stage the flower from 2.0 m above the horizontal floor with initial velocity which is making an angle $${ 37 }^{ \circ  }$$ above the horizontal. The height of stage above the horizontal floor is (g = $${ 10 }ms^{ -2 }$$)
  • 9.75 m
  • 15 m
  • 10.25 m
  • 12 m
Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/ s and 40 m /s, respectively.  Which of the following graph best represents the time variation of relative position of the second stone with respect  to the first ? ( Assume stones do not rebound after hitting the ground and neglect air resistance, take $$g = 10 m/s^{2}$$  )
A stone is thrown vertically upwards and caught at the point of projection after 10 seconds.The time taken by the stone to reach the highest point is.
  • 5 sec
  • 10 sec
  • 9.8 sec
  • 4.9 sec
An object is projected with a velocity of 20$$\mathrm { m } / \mathrm { s }$$ making an angle of $$45 ^ { \circ }$$ with horlzontalThe equation for the trajectory is $$h = A x - B x ^ { 2 }$$ where $$h$$ is height, $$x$$ is horizontal distancy $$A$$ and $$B$$ are constants. The ratio $$A : B$$ is $$\left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right)$$ 
  • $$1 : 5$$
  • $$5 : 1$$
  • $$1 : 40$$
  • $$40 : 1$$
A projectile is fired from a horizontal ground. The coefficient of restitution between projectile are ground is $$e$$. If $$\left( T _ { 1 } , H _ { 1 } , R _ { 1 } \right) \text { and } \left( T _ { 2 } , H _ { 2 } , R _ { 2 } \right)$$ are (time of flight, maximum height, horizontal range) first two collisions with the ground, then
(i)$$\frac { T _ { 1 } } { T _ { 2 } } = \mathrm { e }$$
(ii)$$\frac { T _ { 1 } } { T _ { 2 } } = \frac { 1 } { e }$$
(iii)$$\frac { R _ { 1 } } { R _ { 2 } } = \frac { 1 } { e }$$
(iv)$$\frac { H _ { 1 } } { H _ { 2 } } = \frac { 1 } { e ^ { 2 } }$$
1429880_d453e5e691674c40b83a70dd6e839f6a.png
  • only $$( i ) , ( ii ) , ( iv)$$ are correct
  • only $$( ii ) , ( iii ) , ( iv)$$ are correct
  • only $$( ii ), (iii)$$ are correct
  • only $$( i ) , ( iv)$$ are correct

A Body of mass m, moving along the positive X-direction is subjected to a resistive force $$F = K{v^2}$$  ( where K is a constant and v the particle velocity). If $$m = 10kg,v = 10m/s\;{\text{at}}\;t = 0,\;{\text{and}}\;K = 2N/{m^2} - {s^{ - 2}}$$ the velocity when t = 2s is 
  • $$\dfrac{{10}}{3}m/s$$
  • 2 m/s
  • $$-\dfrac{{10}}{3}m/s$$
  • $$\dfrac{{3}}{10}m/s$$
The path followed by a body projected along y axis is given by $$y =\sqrt{3}x - {(1/2)} x^2$$. If $$g =10 m/s^2$$, then the initial velocity pf projectile will be -(x and y are in m)
  • $$3\sqrt{10} m/s$$
  • $$2\sqrt{10} m/s$$
  • $$10\sqrt{3} m/s$$
  • $$10\sqrt{2} m/s$$
A projectile is projected on a inclined plane of inclination $$ 30^0 $$ with speed of $$ 20 ms^{-1} $$ to an angle $$ 30^0 $$ with inclined plane. find time of flight.
1444528_e52badf8488b4fda85ba3af490e8d228.png
  • $$ \dfrac {2}{ \sqrt 3} $$
  • $$ \dfrac {4}{ \sqrt 3} $$
  • $$ 4 $$
  • $$ \dfrac {5}{ \sqrt 3} $$
For an object to move in uniform circular motion, it is necessary to have 
  • Zero net force
  • Net force in the radial inward direction
  • Net force in the radial outward direction
  • Net force in a tangential direction
The normal component of acceleration of a particle in circular motion:
  • changes the speed of the particle only
  • changes the direction of velocity only
  • is along the direction of velocity
  • is away from the centre.

A projectile is projected perpendicular to the shown inclined plane then its time of flight will be


1413918_2d0b5c34be80461e9c0c3403d11d0a96.PNG
  • $$4\sqrt 3 {\text{s}}$$
  • $$8\sqrt 3 {\text{s}}$$
  • 4 s
  • 8 s
The position of particle expressed as $$\vec { r } =(2{ t }^{ 3 }\hat { i } +t\hat { j } )$$m, where t is time in second.The average velocity during first 2 seconds starting from t=0 and origin is given by 
  • $$(12\hat { i } +\hat { j } )$$ m/s
  • $$(8\hat { i } +\hat { j } )$$ m/s
  • $$(\hat { i } +\hat { j } )$$ m/s
  • $$(2\hat { i } +\hat {3 j } )$$ m/s
The horizontal and vertical displacements of a projectile are given as $$x = at$$ & $$y = bt - ct^2$$. Then velcocity of projection is 
  • $$\sqrt{a^2+b^2}$$
  • $$\sqrt{b^2+c^2}$$
  • $$\sqrt{a^2+c^2}$$
  • $$\sqrt{b^2-c^2}$$
If vector $$\vec{A}=(\hat{i}+2\hat{j}+3\hat{k})m$$ and $$\vec{B}=(-\hat{i}+-\hat{j}+-\hat{k})m$$ represents two sides of a triangle, then the third side can have length equal to :-
  • $$\sqrt{5}$$
  • $$8m$$
  • $$6m$$
  • Both $$(1)$$ and $$(3)$$
If $$z=4+i\sqrt { 7 } $$, then the value of $${ Z }^{ 3 }-{ 4Z }^{ 2 }-9Z+91$$ is 
  • $$4-i\sqrt { 7 } \quad $$
  • -1
  • 91
  • NONE
An object initially at position $$2\hat{i}+5\hat{j}+\hat{k}$$ is given a displacement $$8\hat{i}-2\hat{j}+\hat{k}$$. The co-ordinates of final position are :-
  • $$(10, 3, 2)$$
  • $$(6, 3, 0)$$
  • $$(10, 7, 2)$$
  • $$(6, 3, 2)$$
A stone tied at the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25s, what is the magnitude of acceleration of the stone
  • $$9.91 m/s^2$$
  • $$10.20 m/s^2$$
  • $$1.10 m/s^2$$
  • $$1.20 m/s^2$$
The three $$\bar { A } =3\hat { i } -2\hat { j } +\hat { k } ,\bar { B } =\hat { i } -3\hat { j } +5\hat { k } $$ and $$\bar { C } =2\hat { i } +\hat { j } -4\hat { k } $$ form 
  • An equilateral triangle
  • Isosceles triangle
  • A right angled triangle
  • No triangle
Figure shows a circular path taken by a particle. If the instantaneous velocity of the particle is $$v=-\left( 3m/s \right) \hat { i } +\left( 3m/s \right) \hat { j } $$. Through which quadrant is the particle moving when it is travelling clockwise. 
1464606_e22c6deea8bf4411b7c1c8dd0633c0d3.JPG
  • First
  • Second
  • Third
  • Fourth
An aeroplane is moving in a circular path with a speed 250 km/hr; What is the change is velocity in half revolution ? 
  • 500 km/hr
  • 250 km/hr
  • 125 km/ hr
  • zero
v-t graph of an object of mass 1 kg is shown. Select the wrong statement-
1533041_ff426a6b5ecf426f83b9bf11aea4c79f.PNG
  • Work done on the object in 30 s is zero
  • The average acceleration of the object is zero
  • The average velocity of the object is zero
  • The average force on the object is zero
The displacement of a body of mass 2kg varies with time $$t$$ as $$S=t^2+ 2t$$, where $$S$$ is in metres and t is in seconds. The work done by all the forces acting on the body during the time interval
t 2s tot 4s is:
  • $$36$$ J
  • $$64$$ J
  • $$100$$ J
  • $$120$$ J
A body is thrown horizontally from the top of a tower. It reaches the ground after $$2s$$, strike at an angle of $$45^0$$ with horizontal . The velocity of projection is 
  • $$19.6m/s$$
  • $$9.8m/s$$
  • $$9.8\sqrt{2}m/s$$
  • $$9.8/\sqrt{2}m/s$$
Two toy cars of masses $$m_1$$ and $$m_2$$ are moving along the circular paths of radii $$r_1$$ and $$r_2$$. They cover equal distances in equal times. The ratio of angular velocities of two cars will be:
  • $$m_1:m_2$$
  • $$r_1:r_2$$
  • $$1:1$$
  • $$m_1r_1:m_2r_2$$
A vehicle is moving on a road with an acceleration $$a=20m/s^{2}$$  as shown in the figure. The frictional coefficient between the block of mass $$m$$ and the vehicle, so that block does not fall downward is $$(g = 10 m/s^{2})$$

1564984_0e80791a4182456e8d7bd2c5309fa8b1.PNG
  • $$0.5$$
  • $$0.4$$
  • $$0.3$$
  • $$0.1$$
Two particles $$A$$ and $$B$$ are projected simultaneously in the directions as shown in the figure with velocities $$v_A = 25\ m/s$$ and $$v_B =10\sqrt 3\ m/s$$. If they collide in air after $$2\ s$$, the angle $$\theta$$ is:
1565068_e1d106afc3f846ad9900bbe10f528d30.png
  • $$30^\circ$$
  • $$45^\circ$$
  • $$53^\circ$$
  • $$37^\circ$$
It is possible to project a particle with a given velocity in two possible ways so as to make it pass through a point at a distance $$r$$ from the point of projection. The product of times taken to reach this point in the two possible ways is then proportional to
  • $$r$$
  • $$r^{2}$$
  • $$\dfrac {1}{r}$$
  • $$\dfrac {1}{r^{2}}$$
The velocity of a projectiole at  the initial point A is  $$(2\hat{i}+3\hat{j})$$  m/s. Its velocity ( in m/s) at point B is 
1605548_e89142d5cad64163969a1bc9110f4990.png
  • $$2\hat{i}-3\hat{j}$$
  • $$-2\hat{i}-3\hat{j}$$
  • $$-2\hat{i}+3\hat{j}$$
  • $$2\hat{i}+3\hat{j}$$
In a Carnot engine, the temperature of the source is found to be $$727$$ $$^{0}$$C and that of the sink to be $$27$$ $$^{0}$$C the approximate efficiency of the engine
  • $$70$$ %
  • $$30$$ %
  • $$60$$ %
  • $$90$$ %
A stone of mass $$1\ kg$$ tied to a light inextensible string of length $$L=\dfrac{10}{3}$$ is whirling in a circular path of radius L in vertical plane. If the ratio of the maximum tension to the minimum tension in the string is $$4$$, what is the speed of stone at the highest point of the circle? (Taking $$g=10\ m/s^2$$)
  • $$10\ m/s^{-1}$$
  • $$5\sqrt{2}\ m/s^{-1}$$
  • $$10\sqrt{3}\ m/s^{-1}$$
  • $$20\ m/s^{-1}$$
A particle projected at an angle $$\theta$$ with the horizontal from the centre of the floor of a cylindrical room of radius $$\tau$$ returns to the point of projection after three elastic collisions with the walls and ceiling. If the particle remains in air for time T, find the speed of projection.
1731070_e6c752357aea49179fcf5c557b79965f.PNG
  • $$\frac{3r}{T \ \cos\theta}$$
  • $$\frac{4r}{T \ \cos\theta}$$
  • $$2\sqrt{\frac{gr}{2 \ \sin\theta}}$$
  • $$>2\sqrt{\frac{gr}{ \ \sin2\theta}}$$
A solid body rotates about a stationary axis so that its angular velocity depends on the rotational angle $$\phi$$ as $$\omega =\omega_0-k\phi$$ where $$\omega_0$$ and k are positive constants. At the moment $$t=0, \phi =0$$, the time dependence of rotation angle is?
  • $$k\omega_0e^{-kt}$$
  • $$\dfrac{\omega_0}{k}e^{-kt}$$
  • $$\dfrac{\omega_0}{k}(1-e^{-kt})$$
  • $$\dfrac{k}{\omega_0}(e^{-kt}-1)$$
The particle is moving along a circular path as shown in Figure. The instantaneous velocity of the particles is
$$\vec v =(4\ ms^{-1})\hat i -(3\ ms^{-1}\hat j$$
Through which quadrants does the particle move when it travels clockwise and anticlockwise, respectively, around the circle?
1734500_171a82877d674763a8a592de7e59b260.png
  • First, first
  • First, second
  • First, third
  • Third, first
0:0:1


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