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

A radio-controlled toy car travels along a straight line for a time of $$15s$$. The variation with time t of the velocity v of the car is shown.
What is the average velocity of the toy car for the journey shown by the graph?

1648396_b4983ad1609d4323a7c002ebba5847db.png
  • $$-1.5 ms^{-1}$$
  • $$0.0 ms^{-1}$$
  • $$4.0 ms^{-1}$$
  • $$4.5 ms^{-1}$$
The vector sum of the forces of 10 newton and 6 newton can be:
  • 2N
  • 8N
  • 18N
  • 20N
The height y and the distance X along the horizontal for a body projected in the vertical plane given by $$y=8t-{ 5t }^{ 2 }$$ and $$x=6t.$$ Then initial velocity of the projected body is $$\left( g=10{ ms }^{ -2 } \right) .$$
  • $${ 8ms }^{ - 1}$$
  • $${ 4ms }^{ -1 }$$
  • $${ 10ms }^{ -1 }$$
  • $${ 10/3ms }^{ - 1}$$
The position vector of a particle changes with time according to the relation $$\vec{r}(t)=15t^2\hat{i}+(4-20t^2)\hat{j}$$. What is the magnitude of the acceleration at $$t=1$$?
  • $$40$$
  • $$100$$
  • $$25$$
  • $$50$$
The position vector of a point P is $$\overrightarrow r=x \overrightarrow i + y \overrightarrow j+x \overrightarrow k$$, Where $$x,y,z,\epsilon N$$ and $$\overrightarrow a= \overrightarrow i+ \overrightarrow j+\overrightarrow k$$. If $$\overrightarrow r. \overrightarrow a=10$$, then the number of possible positions of P is ___________.
  • $$30$$
  • $$72$$
  • $$66$$
  • $$36$$
A particle starts from points A with constant speed V on a circle of radius R find magnitude of average velocity after half revolution 
  • $$ \frac {2v}{\pi} $$
  • $$ \frac {3v}{4\pi} $$
  • $$ 3 \sqrt {3v} $$
  • $$ \frac { 3\sqrt { 3v } }{ 2\pi } $$
A projectile thrown with an initial velocity of $$10 ms^{-1}$$ at an angle $$\alpha$$ with the horizontal, has a range of $$5 m.$$ Taking $$g = 10 ms^{-2}$$ and neglecting air resistance, what will be the estimated value of $$\alpha$$ ? 
  • $$15^o$$
  • $$30^o$$
  • $$45^o$$
  • $$75^o$$
If the length of second's hand of a clock is $$10\, cm$$, the speed of its tip (in $$cm\, s^{-1}$$) is nearly 
  • $$2$$
  • $$0.5$$
  • $$1.5$$
  • $$1$$
The real force $$F$$ acting on a particle of mass $$m$$ performing circular motion acts along the radius of circle $$r$$ and is directed towards the center of circle. The square root of magnitude of such force is? ($$T =$$ Time Period)
  • $$\dfrac{2\pi}{T}\sqrt{mr}$$
  • $$\dfrac{Tmr}{4\pi}$$
  • $$\dfrac{2\pi T}{\sqrt{mr}}$$
  • $$\dfrac{T^2mr}{4\pi}$$
If the position vector $$\vec{a}$$ of point $$(12, n) $$ is such that $$\left | \vec{a} \right | = 13$$, then find the value (s) of $$n$$.
  • $$\pm 6$$
  • $$\pm 4$$
  • $$\pm 5$$
  • $$\pm 7$$
The minimum magnitude of resultant force is
  • $$= 0$$
  • $$> 0$$
  • $$< 0$$
  • $$\leq 0$$
A person from a truck, moving with a constant speed of $$60$$ km/h, throws a ball upwards with a speed of $$60$$ km/h. Neglecting the effect of Earth and choose the correct answer from the given choice.
  • The person cannot catch the ball when it comes down since the truck is moving
  • The person can catch the ball when it comes down, if the truck is stopped immediately after throwing the ball
  • The person can catch the ball when it comes down, if the truck moves with speed less than $$60$$ km/h but does not stop
  • The person can catch the ball when it comes down, if the truck moves with speed more than $$60$$ km/h
  • The person can catch the ball when it comes down, if the truck continues to move with a constant speed of $$60$$ km/h
If electric current is assumed as vector quantity, then :
  • Charge conservation principle fails
  • Charge conservation principle does not fail
  • Coulomb's law fails
  • None of the above
A particle has a velocity $$u$$ towards east at $$t=0$$. Its accelerations towards west and is constant. Let $$x_{A}$$ and $$x_{B}$$ be the magnitude of displacement in the first $$10$$ seconds and the next $$10$$ seconds
  • $$x_{A} < x_{B}$$
  • $$x_{A}=x_{B}$$
  • $$x_{A}>x_{B}$$
  • the information is insufficient to decide the relation of $$x_{A}$$ with $$x_{B}$$
A situation may be described by using different sets of coordinate axes having different orientations. Which of the following do not depend on the orientation of the axes?
  • The value of a scalar
  • Component of a vector
  • A vector
  • The magnitude of a vector
A stone is projected upwards and it returns to ground on a parabolic path. Which of the following remains constant?
  • Speed of the ball
  • Horizontal component of velocity
  • Vertical component of velocity
  • None of the above
Mark correct option or options:
  • Radial acceleration is equal to time derivative of radial velocity.
  • Radial acceleration is not equal to time derivative of radial velocity
  • Transverse acceleration is time derivative of transverse velocity
  • Both $$(b)$$ and $$(c)$$ are correct
What is the $$\nabla  \Phi$$ at the point $$(0, 1, 0)$$ of a scalar function $$\Phi$$, if $$\Phi = 2x^{2} + y^{2} + 3z^{2}$$?
  • $$2\hat {j}$$
  • $$3\hat {j}$$
  • $$4\hat {i} + 2\hat {j}$$
  • $$3\hat {i} + 3\hat {j}$$
If a number of particles are projected from the same point in the same plane so as to describe equal parabolas, then the vertices of their paths lie on a:
  • Parabola
  • Circle
  • Square
  • Rectangle
A particle is projected at an angle $$60^o$$ with the horizontal with a speed $$10$$ m/sec. Then latus rectum is: (Take $$g=10m/s^2$$)
1702938_f0f7d82ef38846f7b9b359650885bea5.png
  • $$5$$ m
  • $$15$$ m
  • $$10$$ m
  • $$0$$
Two buses A and B are moving around concentric circular paths of radii $$r_A$$ and $$r_B$$. If the two buses complete the circular paths in the same time, the ratio of their linear speeds is?
  • $$1$$
  • $$\dfrac{r_A}{r_B}$$
  • $$\dfrac{r_B}{r_A}$$
  • None of these
In figure the angle of inclination of the inclined plane is $$30^o$$. Find the horizontal velocity $$V_0$$ so that the particle hits the inclined plane perpendicularly.
1734529_437967c956c34ed993048fd79daca279.png
  • $$V_0 =\sqrt {\dfrac {2gH}{5}}$$
  • $$V_0 =\sqrt {\dfrac {2gH}{7}}$$
  • $$V_0 =\sqrt {\dfrac {gH}{5}}$$
  • $$V_0 =\sqrt {\dfrac {gH}{7}}$$
Mark the correct statement.
  • $$|\vec{a} + \vec{b}| \geq |\vec{a}| +| \vec{b}|$$
  • $$|\vec{a} + \vec{b}| \leq |\vec{a}| +| \vec{b}|$$
  • $$|\vec{a} - \vec{b}| \geq |\vec{a}| +| \vec{b}|$$
  • All of the above
Which of the following two statements is more appropriate:
(A) Two velocities are added using the triangle rule because velocity is a vector quantity.
(B) Velocity is a vector quantity because two velocities are added using the triangle rule.
  • Statement A
  • Statement B
  • Both A and B
  • None of these
A. stone is thrown horizontally with a velocity of 10 m/ s at t = The radius of curvature of the stone's trajectory at t = 3 s is : $$ [ take g = 10 m/s^2 ] $$
  • $$ 10\sqrt {10} m $$
  • $$ 100 m $$
  • $$ 100 \sqrt {10} m $$
  • $$ 1000 m $$
The resultant of $$\underset{A}{\rightarrow}$$ and $$ \underset{B}{\rightarrow} $$ prependicular to $$ \underset{A}{\rightarrow} $$ what is a angle between $$ \underset{A}{\rightarrow} $$ and $$ \underset{B }{\rightarrow} $$ 
  • $$ cos^{-1}\left ( \dfrac{a}{b} \right ) $$
  • $$ cos^{-1}\left ( -\dfrac{a}{b} \right ) $$
  • $$ sin^{-1}\left ( \dfrac{a}{b} \right ) $$
  • $$ sin^{-1}\left ( -\dfrac{a}{b} \right ) $$
A body is undergoing uniform. circular motion then which of the following quantity is constant :
  • velocity
  • acceleration
  • force
  • kinetic energy
Which of the following two statement is not more appropriate
(a) Two volecities is added using triangle rule because velocity is vector quantity.
(b) velocity is vector quantity because two velocity are added using triangle rule
  • (a)
  • (b)
  • (a) and (b)
  • None of this
A plane is revolving around the earth with a speed if $$100\ km/hr$$ at a constant height from the surface of earth. The change in the velocity as it travels half circle is 
  • $$200\ km/hr$$
  • $$150\ km/hr$$
  • $$100\sqrt 2\ km/hr$$
  • $$0$$
A particle is moving in a circular path of radius $$r$$. The displacement after half a circle would be:
  • Zero
  • $$\pi r$$
  • $$2r$$
  • $$2\pi r$$
Figure below show a body of mass $$M$$ moving with the uniform speed on a circular path of radius, $$R$$. What is the change in acceleration in ging from $$P_1$$ to $$P_2$$
1811810_09291fabbdb046de98f3fff29610edc9.png
  • Zero
  • $$v^2/2R$$
  • $$2v^2/R$$
  • $$\dfrac{v^2}{R} \times \sqrt 2$$
The position vector of the point which divides the join of points with position vectors $$\vec a +\vec b$$ and $$2\vec a-\vec b$$ in the ratio $$1:2$$ is
  • $$\dfrac {3\vec a+2\vec b}{3}$$
  • $$\vec a$$
  • $$\dfrac {5\vec a-\vec b}{3}$$
  • $$\dfrac {4\vec a+\vec b}{3}$$
In uniform circular motion
  • Both the angular velocity and the angular momentum vary
  • The angular velocity varies but the angular momentum remains
    constant
  • Both the angular velocity and the angular momentum stay
    constant
  • The angular momentum varies but the angular velocity remains
    constant
Which of the following is a vector
  • Pressure
  • Surface tension
  • Momentum of inertia
  • None of these
A particle is moving in a circle with uniform speed. Its motion is
  • Periodic and simple harmonic
  • Periodic but not and simple harmonic
  • A periodic
  • None of the above
Velocity of a body on reaching the point from which it was projected upwards, is 
  • $$ \nu = 0 $$
  • $$ \nu = 2u $$
  • $$ \nu = 0.5 u $$
  • $$ \nu = u $$
Which of the following is not a scalar quantity ?
  • Time
  • Volume
  • Displacement
  • Work
Let $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$ be unit vectors inclined at an variable angle $$\theta \left( \theta \epsilon \left(  0,\frac{\pi}{2} \right)(\frac{\pi}{2}, \pi) \right).$$
Let $$g(\theta)=  {\int}_{-(\overrightarrow{a}.\overrightarrow{b})^2}^{-\lambda} f^2(x)dx+ {\int}_{\lambda}^{|\overrightarrow{a}\times \overrightarrow{b}|^2} f^2(x)dx-\frac{2}{\lambda}, where \lambda > 0 , $$is function satisfying $$ \displaystyle f(x)+f(y)=\frac{x+y}{xy},  x, y\epsilon R-[0] \; and \; h(\theta)=-g(\theta)+|\overrightarrow{a}\times \overrightarrow{b}|^2.(\overrightarrow{a}. \overrightarrow{b}_1)^2, \overrightarrow{b}_1 = 2\overrightarrow{b}$$
If $$|g(\theta)|$$ is attaining its minimum value, then minimum distance between origin and the point of intersection of lines $$\overrightarrow{r}\times \overrightarrow{a}=\overrightarrow{a}\times \overrightarrow{b}$$ and $$\overrightarrow{r}\times \overrightarrow{b} = \overrightarrow{b}\times \overrightarrow{a}$$ is
  • $$\sqrt{2-\sqrt{2}}$$
  • $$\sqrt{2+\sqrt{2}}$$
  • $$\sqrt{\sqrt{2}+1}$$
  • $$\sqrt{\sqrt{2}-1}$$
How much deep inside a man should go so that his weight becomes one forth of that point which is at height $$R$$ above the surface of the earth.

  • $$\mathrm{R}/4$$
  • $$15\mathrm{R}/16$$
  • $$3\mathrm{R}/4$$
  • $$\mathrm{R}/2$$
A particle projected from O and moving freely under gravity strikes the horizontal plane passing through O at a distance R from the starting point O as shown in the figure. Then

72300.jpg
  • there will be two angles of projection if $$R g < u^{2}$$
  • the two possible angles of projection are complementary
  • the product of the possible times of flight from O to A is $$\frac{2R}{g}$$
  • there will be more than two angles of projection if $$R g = u^{2}$$
A particle moves in the $$x-y$$ plane according to the law $$x = kt, y = kt (1 - \alpha t) $$  where $$k$$ and $$\alpha $$   are positive constants and $$t$$ is time. The trajectory of the particle is:
  • $$y=kx$$
  • $$y=x- \dfrac {\alpha x^{2}}{k}$$
  • $$y=-\dfrac{\alpha x^{2}}{k}$$
  • $$y=\alpha x$$
Velocity of a particle varies as $$\vec{V}=y\hat{i}-x\hat{j}$$ under the effect of a single variable force. Then
  • force on the particle is conservative
  • acceleration of the particle is ( $$x\vec{i}-y \vec{j}$$)
  • particle moves with constant speed
  • possible path of the particle is only a circle
For a particle performing uniform circular motion, choose the correct statement(s) from the following:
  • Magnitude of particle velocity (speed) remains constant.
  • Particle velocity remains directed perpendicular to radius vector.
  • Direction of acceleration keeps changing as particle moves.
  • Angular momentum is constant in magnitude but directionkeeps changing.
Two particles projected from the same point with same speed u at angles of projection $$\alpha$$ and $$\beta$$ strike the horizontal ground at the same point. If $${ h }_{ 1 }$$ and $${ h }_{ 2 }$$ are the maximum heights attained by projectiles, $$R$$ be the range for both and $${ t }_{ 1 }$$ and $${ t }_{ 2 }$$ be their time of flights respectively, then 
  • $$\alpha +\beta =\dfrac { \pi }{ 2 } $$
  • $$R=4\sqrt { { h }_{ 1 }{ h }_{ 2 } } $$
  • $$\dfrac { { t }_{ 1 } }{ { t }_{ 2 } } =tan \alpha $$
  • $$tan\alpha =\sqrt { \dfrac { { h }_{ 1 } }{ { h }_{ 2 } } } $$
What is the tangential acceleration?
  • $$ 3\alpha$$
  • $$ 2\alpha$$
  • $$\alpha$$
  • $$ 4\alpha$$
Two particles move on a circular path (one just inside and the other just outside) with angular velocities $$\omega $$ and $$ 5 \omega $$ starting from the same point. Then:
  • they cross each other at regular intervals of time $$\displaystyle \frac{\pi }{2 \omega }$$ when their angular velocities are directed opposite to each other
  • they cross each other at points on the path subtending an angle of 60$$^o$$ at the centre if their angular velocities are directed opposite to each other
  • they cross at intervals of time $$\displaystyle \frac{\pi }{3 \omega }$$ if their angular velocities are directed opposite to each other
  • they cross each other at points on the path subtending $$90^{\circ}$$ at the centre if their angular velocities are similar to each other
A body projected vertically upward with a velocity $$v$$ at $$t=0$$ is found at a height $$h$$ after $$1$$ second and after further $$6$$ seconds, it is found at the same height ($$g=10ms^{-2}$$). Then,
  • $$h$$ is $$30 m$$
  • $$v$$ is $$40 m/s$$
  • maximum height is $$80 m$$
  • distance moved in $$5th$$ second is $$5 m$$
Particles P and Q are undergoing uniform horizontal circular motions along concentric circles of different radii in clockwise sense. P completes each round in 2 minutes while Q does it in 5 minutes. Time required by Q to make one revolution around P is

  • 3 minutes
  • 10 minutes
  • 10/3 minutes
  • This is not possible as Q is moving slower than P.
A particle has initial velocity, $$\displaystyle \vec{v}=3\hat{i}+4\hat{j}$$ and a constant force $$\displaystyle \vec{F}=4\hat{i}-3\hat{j}$$ acts on it. The path of the particle can be:
  • straight line
  • parabolic
  • circular
  • hyperbolic
A particle moves in a circle of radius $$4cm$$ clockwise at constant speed $$2 cm/s$$. If $$\widehat{x}$$ and $$\widehat{y}$$  are unit acceleration vector along x and y-axis respectively (in $$cm/s^2$$), the acceleration of the particle at the instant half way between P and Q is given by
184049_2d8c8e92f0454c8fabc22bf55aae59e0.png
  • $$-4(\widehat{x}+\widehat{y}) $$
  • $$4(\widehat{x}+\widehat{y}) $$
  • $$-(\widehat{x}+\widehat{y})/\sqrt{2} $$
  • $$(\widehat{x}-\widehat{y})/4 $$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Engineering Physics Quiz Questions and Answers