CBSE Questions for Class 11 Engineering Physics Motion In A Plane Quiz 4 - MCQExams.com


$$\overline{\mathrm{R}}$$ is the resultant of vectors $$\vec{A}$$ and $$\vec{B}$$. lf $$\overline R=\displaystyle \frac{\vec B}{\sqrt{2}}$$ the value of $$\theta$$ is :

29365.png
  • 30$$^{0}$$
  • 45$$^{0}$$
  • 60$$^{0}$$
  • 75$$^{0}$$
A projectile is given an initial velocity of $$(\hat{i}+2\hat{j}) \ m/s$$, where $$\hat{i}$$ is along the ground and $$\hat{j}$$ is along the vertical. If $$g=10 \ m/s^{2}$$, the equation of its trajectory is:
  • $$y=2x-5x^{2}$$
  • $$4y=2x-5x^{2}$$
  • $$4y=2x-25x^{2}$$
  • $$y=x-5x^{2}$$
The maximum resultant of two concurrent forces is $$10N$$ and their minimum resultant is $$4N$$. The magnitude of the larger force is:
  • $$5N$$
  • $$7N$$
  • $$3N$$
  • $$14N$$
Match the following : 
List - I List - II
a) Current strengthe) Vectors
b) Distance,Work donef) Scalars
c) Force, torqueg) Possesses direction but not vector
d) Component of vector, smaller value of angular displacementh) Scalar and vector
  • $$\mathrm{a}\rightarrow \mathrm{e};\mathrm{b}\rightarrow \mathrm{f};\mathrm{c}\rightarrow \mathrm{g};\mathrm{d}\rightarrow \mathrm{h}$$
  • $$\mathrm{a}\rightarrow \mathrm{h};\mathrm{b}\rightarrow \mathrm{g};\mathrm{c}\rightarrow \mathrm{f};\mathrm{d}\rightarrow \mathrm{e}$$
  • $$\mathrm{a}\rightarrow \mathrm{g};\mathrm{b}\rightarrow \mathrm{e};\mathrm{c}\rightarrow \mathrm{f};\mathrm{d}\rightarrow \mathrm{h}$$
  • $$\mathrm{a}\rightarrow \mathrm{g};\mathrm{b}\rightarrow \mathrm{f};\mathrm{c}\rightarrow \mathrm{e};\mathrm{d}\rightarrow \mathrm{h}$$
Let $$\vec{A}=2\hat{i}+7\hat{j},\vec{B}=\hat{i}+2\hat{j}+4\hat{k},\ \displaystyle \vec{C}=\dfrac{9\hat{i}+30\hat{j}+4\hat{k}}{5}$$. 
The ratio in which $$\vec{C}$$ divides $$\vec{AB}$$ internally is?
  • $$1:4$$
  • $$2:3$$
  • $$3:2$$
  • $$5:1$$
Speed $$v$$ of a particle moving along a straight line, when it is at a distance $$x$$ from a fixed point on the line is given by
$$v^{2} = 108 - 9x^{2}$$ (assuming mean position to have zero phase constant)
(all quantities in are in $$cgs$$ unit):
  • The motion is uniformly accelerated along the straight line
  • The magnitude of the acceleration at a distance $$3\ cm$$ from the fixed point is $$27\ cm/s^{2}$$
  • The motion is simple harmonic about $$x = \sqrt{12}\ m$$.
  • The maximum displacement from the fixed point is $$4\ cm$$.
Suppose a boy is enjoying a ride on a merry-go-round which is moving with a constant speed of $$10\ ms^{-1}$$. It implies that the boy is :
  • at rest
  • moving with no acceleration
  • in accelerated motion
  • moving with uniform velocity
A mass is performing vertical circular motion(see figure).If The average velocity of theparticle is increased, then at which point thestring will break :
71054.png
  • A
  • B
  • C
  • D
A wheel, starting from rest, rotates with a uniform angular acceleration of $$2  rad s^{-2}$$. The number of rotations it performs in the tenth second is
  • 3
  • 6
  • 9
  • 12
A smooth flat horizontal turntable 4.0 m in diameter is rotating at 0.050 revs per second. A student at the centre of the turntable, and rotating with it, Places a smooth flat puck on the turntable 0.50 m from the edge. Which of the following figures describes the motion of the puck as seen by a stationary observer who is standing at the side of the turntable and above the turntable?
A particle moves on a circular path of radius r. Find the ratio of the magnitude of displacement and the distance covered by the particle when the body moves from one diametric end to the other.
  • 1 : 1
  • $$\pi :2$$
  • $$2:\pi $$
  • $$\pi :1$$
A particle is moving in a circular path of radius $$r$$. The magnitude of displacement after half a circle would be :
  • Zero
  • $$\pi r$$ 
  • $$2 r$$
  • $$2 \pi r$$ 
In a projectile motion from a point of horizontal surface to another point on the same surface (Take $$\vec {a}=$$ acceleration and $$\vec {v}=$$ instantaneous velocity)
  • $$\vec{a}\cdot\vec{v}=0$$ at maximum height
  • $$\vec{a}\cdot \vec{v}=0$$ only if angle of projection is $$90^{\circ}$$
  • $$\vec{a} \times \vec{v}=$$ constant every where in air
  • None of these
A shell fired from the base of a mountain just clears it. If $$\alpha$$ is the angle of projection, then the angular elevation of the summit $$\beta$$ is
120665.png
  • $$\dfrac {1 \alpha}{2}$$
  • $$\tan^{-1}\left (\dfrac {1}{2}\right )$$
  • $$\tan^{-1}\left (\dfrac {1 \tan \alpha}{2}\right )$$
  • $$\tan^{-1}(2 \tan \alpha)$$
A particle is moving in a circular path of radius r. Its displacement after moving through half the circle would be :
  • Zero
  • $$r$$
  • $$2r$$
  • $$\dfrac{2}{r}$$
If air resistance is considered, then the maximum height achieved by the projectile
  • decreases
  • increases
  • remains unchanged
  • very difficult to answer as no data provided
A small body is thrown at an angle to the horizontal with the initial velocity $$\vec{v}_0$$. Neglecting the air drag, find the displacement of the body as a function of time $$r(t)$$.
  • $$\displaystyle\vec{r}=\vec{v}_0t+\dfrac{\vec{g}t^2}{2}$$
  • $$\displaystyle\vec{r}=\vec{v}_0t-\dfrac{\vec{g}t^2}{2}$$
  • $$\displaystyle\vec{r}=2\vec{v}_0t-\dfrac{\vec{g}t^2}{2}$$
  • $$\displaystyle\vec{r}=2\vec{v}_0t+\dfrac{\vec{g}t^2}{2}$$
Find the total acceleration of the point as a function of velocity and the distance covered.
  • $$\sqrt{2}\dfrac{v^2}{R}$$
  • $$\sqrt{2}\dfrac{2v^2}{R}$$
  • $$\sqrt{3}\dfrac{v^2}{R}$$
  • $$\sqrt{3}\dfrac{2v^2}{R}$$
Two projectiles A and B are thrown with the same speed such that A makes angle $$ \theta $$ with the horizontal and B makes angle $$ \theta $$ with the vertical, then
  • Both must have same time of flight
  • Both must achieve same maximum height
  • A must have more horizontal range than B
  • Both may have same time of flight
Suppose a player hits several baseballs. Which baseball will be in the air for the longest time?
  • The one with the farthest range.
  • The one which reaches maximum height.
  • The one with the greatest initial velocity.
  • The one leaving the bat at $$ 45^0 $$ with respect to the ground.
Consider the motion of the tip of the minute hand of a clock. In one hour
  • the displacement is zero.
  • the distance covered is zero.
  • the average speed is zero.
  • the average velocity is zero.
A ball is thrown from a height of $$12.5m$$ from the ground level in the horizontal direction. It falls at a horizontal distance of $$200m$$. The initial velocity of the ball (approximately) is
  • $$140m/s$$
  • $$80m/s$$
  • $$126m/s$$
  • $$120m/s$$
In uniform circular motion
  • acceleration is variable.
  • acceleration is uniform.
  • the direction and magnitude of acceleration both vary.
  • if force applied is doubled in circular motion, then angular velocity becomes double.
Find the angle between the vectors of the angular velocity and the angular acceleration at $$t=10.0\:s$$
  • $$15^\circ$$
  • $$14^\circ$$
  • $$17^\circ$$
  • $$13^\circ$$

Two vectors $$\overline{A}$$ and $$\overline{B}$$ lie in a plane. Another vector $$\overline{C}$$ lies outside this plane, then the resultant of the three vectors $$(\overline{A}+\overline{B}+\overline{C})$$ :
  • can be of zero magnitude
  • cannot be of zero magnitude
  • lies in the plane containing $$(\overline{A}+\overline{B})$$
  • lies in the plane containing $$(\overline{A}-\overline{B})$$
If the resultant of three vectors is zero then:
  • the magnitude of one vector must be equal to the sum of magnitudes of the other two
  • the magnitude of each vector must be greater than the sum of magnitudes of the other two vectors
  • the magnitude of each vector must be less than the sum of magnitudes of the other two vectors
  • all the three vectors must be of equal magnitude
Two particles A and B are moving on different concentric circles with different velocities $$v_A$$ and $$v_B$$ then angular velocity of B relative to A as observed by A is given by :

134701_e236cc246d664a6aa0f60bb690a00ad4.png
  • $$\displaystyle \frac{v_B - v_A}{r_B - r_A}$$
  • $$\displaystyle \frac{v_A}{r_A}$$
  • $$\displaystyle \frac{v_A - v_B}{r_A - r_B}$$
  • $$\displaystyle \frac{v_B + v_A}{r_B + r_A}$$
A body is moving with uniform speed $$v$$ on a horizontal circle from A as shown in the figure. Change in the velocity in the first quarter revolution is:

134697_48d657f272824c2588b29d8c9e145ce8.jpg
  • $$v^2$$
  • $$\sqrt{2} v$$ southwest
  • $$\sqrt{2}$$ northwest
  • $$2v$$ west
A particle moves in a circle of radius 4 cm clockwise at constant speed of 2 cm $$s^{-1}$$. If $$\hat{x}$$ and $$\hat{y}$$ are unit acceleration vectors along x and y axes, respectively, the acceleration of the particle at the instant half way between PQ is given by

134728.jpg
  • $$-4(\hat{x} - \hat{y})$$
  • $$4(\hat{x} + \hat{y})$$
  • $$\displaystyle \frac {-(\hat{x} + \hat{y})}{\sqrt{2}}$$
  • $$\displaystyle \frac {\hat{x} - \hat{y}}{4}$$
The minimum number of coplanar vectors having different non-zero magnitudes can be added to give zero resultant is :
  • 2
  • 3
  • 4
  • 5
If $$\vec {A}=\vec {B}+\vec {C}$$ and the magnitude of $$\vec {A}, \vec {B}$$ and $$\vec {C}$$ are $$5,4$$ and $$3$$ units, respectively, then the angle between $$\vec {A}$$ and $$\vec {C}$$ is:
  • $$\displaystyle \frac{\pi }{2}$$
  • $$\sin ^{-1}(3/4)$$
  • $$\cos^{-1}(3/5)$$
  • $$\cos^{-1}(4/5)$$
When a ceiling fan is switched off, its velocity falls to half in 36 rotations. How many more rotations it will make?
  • 36
  • 24
  • 18
  • 12
If a particle goes from point A to point B in $$1$$ s moving in a semicircle(See figure). The magnitude of  the average velocity is:

135696.jpg
  • 3.14 $$ms^{-1}$$
  • 2 $$ms^{-1}$$
  • 1 $$ms^{-1}$$
  • zero
If the magnitude of vectors $$\overrightarrow{A}$$, $$\overrightarrow{B}$$ and $$\overrightarrow{C}$$ are 12, 5 and 13, respectively and $$\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}$$, then the angle between the vectors $$\overrightarrow{A}$$ and $$\overrightarrow{B}$$ is 
  • $$\pi/4$$
  • $$\pi/3$$
  • $$\pi/2$$
  • zero
The second equation of motion in rotatory motion is
  • $$\displaystyle{S=ut+\frac{at^2}{2}}$$
  • $$\displaystyle{\theta = \omega_1t+\frac{\alpha t^2}{2}}$$
  • $$\displaystyle{\omega^2_2 = \omega^2_1 +2\alpha \theta}$$
  • $$\displaystyle{\omega_2 = \omega_1 +\alpha t}$$
If $$G$$ and $$G'$$ be the centroids of the triangles $$ABC$$ and $$A'B'C'$$ respectively, then $$\overrightarrow { AA' } +\overrightarrow { BB' } +\overrightarrow { CC' } =$$
  • $$\displaystyle \dfrac { 2 }{ 3 } \overrightarrow { GG' } $$
  • $$\overrightarrow { GG' } $$
  • $$2\overrightarrow { GG' } $$
  • $$3\overrightarrow { GG' } $$
Two wheels are constructed, as shown in Figure, with four spokes. The wheels are mounted one behind the other so that an observer normally sees a total of eight spokes but only four spokes are seen when they happen to align with one another. If one wheel spins at 6 rev/min, while other spins at 8 rev/min in same sense, how often does the observer see only four spokes?
149246.png
  • 4 times a minute
  • 6 times a minute
  • 8 times a minute
  • Once in a minute
$$P$$ is a point on the line through the point $$A$$ whose position vector is $$\overrightarrow{a}$$ and the line is parallel to the vector $$\overrightarrow{b}$$. If $$PA=6$$, the position vector of $$P$$ is
  • $$\overrightarrow{a}+6\overrightarrow{b}$$
  • $$\displaystyle \overrightarrow{a}+\dfrac{6}{\left |\overrightarrow{b} \right |}\overrightarrow{b}$$
  • $$\overrightarrow{a}-6\overrightarrow{b}$$
  • $$\displaystyle \overrightarrow{b}+\dfrac{6}{\left |\overrightarrow{a} \right |}\overrightarrow{a}$$
A straight line $$r=a+\lambda b$$ meets the plane $$r.n=0$$ in $$P$$. The position vector of $$P$$ is
  • $$\displaystyle a+\frac { a.n }{ b.n } b$$
  • $$\displaystyle a+\frac { b.n }{ a.n } b$$
  • $$\displaystyle a-\frac { a.n }{ b.n } b$$
  • None of these
What is the work done in $$t$$ seconds by a body of mass $$m$$ moving in a circular path of radius $$r$$ with a constant angular acceleration? Initially the body was at rest.
  • $$m\alpha^2R^2t^2$$
  • $$2\pi mv^2t$$
  • $$\dfrac{1}{2} m\alpha^2R^2t^2$$
  • zero
A car is moving with a speed of $$72\, kmh^{-1}$$. The radius of its wheel its $$50\, cm$$. If its wheels come to rest after $$20$$ rotations as a result of application of brakes, then the angular retardation produced in the car will be
  • $$23.5\,rads^{-2}$$
  • $$0.25\,rads^{-2}$$
  • $$6.35\,rads^{-2}$$
  • $$zero$$
A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first two seconds it rotates through angle $$\theta_1$$. In the next two seconds it rotates through angle $$\theta_2$$. What is the ratio $$\theta_2 / \theta_1$$?
  • $$4$$
  • $$3$$
  • $$2$$
  • $$1$$
A particle is moving along a circular path of radius 5 m and uniform speed 5 $$ms^{-1}$$. What will be the average acceleration when the particle completes half revolution?
  • $$10\pi ms^{-2}$$
  • $$10/\pi ms^{-2}$$
  • $$10 ms^{-2}$$
  • zero
A bullet is fired horizontally with a speed of $$1500\ m/s$$ in order to hit a target $$100\ m$$ away. If $$g=10\ m/s^2 $$. The gun should be aimed 
  • $$15\ cm$$ above the target
  • $$10\ cm$$ above the target
  • $$2.2\ cm$$ above the target
  • directly towards the target
When a lead storage battery is discharged, then:
  • SO$$_2$$ is evolved
  • lead is formed
  • lead sulphate is consumed
  • sulphuric acid is consumed
When a body moves with a constant speed along a circle:
  • no work is done on it
  • no acceleration is produced in the body
  • no force acts on the body
  • its velocity remains constant
Two identical particles are located at $$\overrightarrow{x}$$ and $$ \overrightarrow{y}$$ with reference to the origin of three dimensional co-ordinate system. The position vector of centre of mass of the system is given by
  • $$\overrightarrow { x } - \overrightarrow { y }$$
  • $$\displaystyle \frac {\overrightarrow { x } + \overrightarrow { y }} {{2}}$$
  • $$(\overrightarrow { x } - \overrightarrow { y })$$
  • $$\displaystyle \frac{\overrightarrow { x } - \overrightarrow { y }} {{2}}$$
A wheel initially at rest, is rotated with a uniform angular acceleration. The wheel rotates through an angle $$\theta_1$$ in first one second and through an additional angle $$\theta_2$$ in the next one second. The ratio $$\theta_2/\theta_1$$ is:
  • $$4$$
  • $$2$$
  • $$3$$
  • $$1$$
A gun is aimed at a horizontal target.  It takes $$\dfrac{1}{2} s $$ for the bullet to reach the target. The bullet hits the target $$x$$  meter below the aim. Then $$x$$ is equal to (Take $$g=9.8\ m/s^2$$)
  • $$\dfrac{9.8}{4} m$$
  • $$\dfrac{9.8}{8} m $$
  • $$ 9.8 m $$
  • $$ 19.6 m $$
A body is revolving with a constant speed along a circle .If its direction of motion is reversed but the speed remains the same. Then,
  • the centripetal force will not suffer any change in magnitude
  • the centripetal force will have its direction reversed
  • the centripetal force will not suffer any change in direction
  • the centripetal force would be doubled
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