CBSE Questions for Class 11 Engineering Physics Work,Energy And Power Quiz 6 - MCQExams.com

A force $$F_{x}$$ acts on a particle such that its position $$x$$ changes as shown in figure.
The work done by the particle as it moves from $$x = 0$$ to $$20\ m$$ is
671463_c83bf09a81ba4b8092025f9c24d1f836.png
  • $$37.5\ J$$
  • $$10\ J$$
  • $$15\ J$$
  • $$22.5\ J$$
  • $$45\ J$$
A particle is moving in a vertical circle. The tension in the string when passing through two platform at angles $$\displaystyle 30^o$$ and $$\displaystyle 60^o$$ vertical (lowest position) are $$T_1$$ and $$T_2$$ respectively
  • $$\displaystyle T_1 = T_2$$
  • $$\displaystyle T_2 > T_1$$
  • $$\displaystyle T_1 > T_2$$
  • Tension in the string always remain the same
A stone of mass m is tied to a string and is moved in a vertical circle of radius r making n revolution per minute. The total tension in the string when the stone is at its lowest point is
  • $$mg$$
  • $$m(g+\pi n r^2)$$
  • $$m(g+ n r)$$
  • $$m(g+ \frac{\pi^2 n^2 r} {900})$$
A particle moves along X-axis from $$x = 10$$ to $$x = 5\ cm$$ under the influence of force given by $$F = (7 - 2x + 3x^{2}) N$$. The work done in the process is
  • $$70\ J$$
  • $$270\ J$$
  • $$35\ J$$
  • $$135\ J$$
A weightless thread can bear tension up to $$3.7$$kg wt. A stone of mass $$500$$g is tied to it and revolved in a circular path of radius $$4$$m in a vertical plane. If $$g=10m/s^2$$, then the maximum angular velocity of the stone will be :
  • $$4rad/s$$
  • $$2rad/s$$
  • $$6rad/s$$
  • none of these
A body of mass m is moving in a circle of radius r with a constant speed $$v$$. If a force $$\dfrac{mv^2}{r}$$ is acting on the body towards the centre, then what will be the work done by this force in moving the body over half the circumference of the circle?
  • Zero
  • $$\dfrac{mv^2}{r^2}$$
  • $$\dfrac{mv^2}{r^2}\times \pi r$$
  • $$\dfrac{\pi r^2}{mv^2}$$
A particle tied to a string describes a vertical circular motion of radius r continually. If it has a velocity $$\sqrt{3gr}$$ at the highest point, then the ratio of the respective tensions in the string holding it at the highest and lowest points is
  • 4 : 3
  • 5 : 4
  • 1 : 4
  • 3 : 2
  • 1 : 2
A pendulum string of length $$l$$ is moved upto a horizontal position and released as shown in figure. If the mass of pendulum is $$m$$, then what is the minimum strength of the string that can withstand the tension as the pendulum passes through the position of equilibrium? 
(neglect mass of the string and air resistance)
682862_25b101d2096244a0bf09864fdbdfb98d.PNG
  • $$mg$$
  • $$2mg$$
  • $$3mg$$
  • $$5mg$$
Two equal masses are attached to the two ends of a spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass during the above stretching is?
  • $$\displaystyle\frac{1}{2}kx^2$$
  • $$-\displaystyle\frac{1}{2}kx^2$$
  • $$\displaystyle\frac{1}{4}kx^2$$
  • $$-\displaystyle\frac{1}{4}kx^2$$
A simple pendulum with bob of mass $$m$$ and length $$x$$ is held in position at an angle $$1$$ and then angle $$2$$ with the vertical. When released from these positions, speeds with which it passes the lowest positions are $${v}_{1}$$ and $${v}_{2}$$ respectively. Then, $$\cfrac { { v }_{ 1 } }{ { v }_{ 2 } } $$ is 
  • $$\cfrac { 1-\cos { { \theta }_{ 1 } } }{ 1-\cos { { \theta }_{ 2 } } } $$
  • $$\sqrt { \cfrac { 1-\cos { { \theta }_{ 1 } } }{ 1-\cos { { \theta }_{ 2 } } } } $$
  • $$\sqrt { \cfrac { 2gx(1-\cos { { \theta }_{ 1 } } ) }{ 1-\cos { { \theta }_{ 2 } } } } $$
  • $$\sqrt { \cfrac { 1-\cos { { \theta }_{ 1 } } }{ 2gx(1-\cos { { \theta }_{ 2 } } ) } } $$
When a rubber -band is stretched by a distance x,it exerts a restoring force of magnitude $$F= ax + bx^2$$ where a and b are constants. the work done is stretching the unstretched rubber band by L is : 
  • $$\dfrac {aL^{2}}{2}+\dfrac{bL^{3}}{3}$$
  • $$\dfrac{1}{2} \begin {pmatrix} \dfrac{aL^2}{2} + \dfrac{bL^3}{3}\end {pmatrix} $$
  • $$aL^2 + bL^3$$
  • $$\dfrac {1}{2} ( aL^2 + bL^3)$$
A block of mass $$M$$ at the end of the string is whirled round a vertical circle of radius $$R$$. The critical speed of the block at the top of the swing is
  • $${ \left( R/g \right) }^{ 1/2 }$$
  • $$g/R$$
  • $$M/Rg$$
  • $${ \left( Rg \right) }^{ 1/2 }$$
The mass of bucket full of water is 15 kg . It is being pulled up from a 15 m deep well. Due to a hole in the bucket 6 kg water flows out of the bucket at a uniform rate. The work done in drawing the bucket out of the well will be $$(g=10 m/s^2)-$$
  • 900 J
  • 1500 J
  • 1800 J
  • 2100 J
If the force constant of a wire is $$K$$, the work done in increasing the length of the wire by/ is
  • $$Kl/ 2$$
  • $$Kl$$
  • $$KI^{2}/2$$
  • $$Kl^{2}$$
The work done by external agent in stretching a spring of force constant $$k = 100\ N/cm$$ from deformation $$x_{1} = 10$$ to deformation $$x_{2} = 20\ cm$$.
  • $$-150\ J$$
  • $$50\ J$$
  • $$150\ J$$
  • None of these
A particle is projected so as to just move along a vertical circle of radius $$r$$ with the help of the massless string. The ratio of the tension in the string when the particle is at the lowest and highest point on the circle is?
  • $$1$$
  • Finite but large
  • Zero
  • Infinite
The diagram below shows the path taken by a ball when Sundram kicks it. The potential energy of the ball is highest at ______________
803001_b9ed29417fbc4db7ab3af6eedc4f5b42.JPG
  • P
  • Q
  • R
  • S
When the speed of a body is doubled, its kinetic energy becomes 
  • Double
  • Half
  • Quadruple
  • One-fourth
A force acts on a $$3 g$$ particle in such a way that position of the particle as a function of time is given by $$x=3t-4t^2+t^3$$, where x is in metre and t is in sec. The work done during the first $$4s$$ is
  • 570 mJ
  • 450 mJ
  • 490 mJ
  • 528 mJ
A particle is tied to one end of a light inextensible string and is moved in a vertical circle, the other end of the string is fixed at the centre. Then for a complete motion in a circle, which is correct.
(air resistance is negligible).
  • Acceleration of the particle is directed towards the centre
  • Total mechanical energy of the particle and earth remains constant
  • Tension in the string remains constant
  • Acceleration of the particle remains constant
A triangular block ABC of mass m and sides 2a lies on a smooth horizontal plane as shown in the figure. Three point masses of mass m each strike the block at A, B and C with speeds v as shown. After the collision, the particles come to rest. Then the angular velocity acquired by the triangular block is (I is the moment of inertia of the triangular block about G, perpendicular to the plane of the block)

770673_c702eef1a2504ddb9734a5e0fa5511d1.png
  • $$\displaystyle 2mva \frac{(1 + \sqrt{3})}{\sqrt{3} l}$$ clockwise
  • $$\displaystyle \frac{2mva}{ l}$$ clockwise
  • $$\displaystyle \frac{2 \sqrt{3} mva}{ l}$$ clockwise
  • None of these.
A simple pendulum of length $$L$$ carries a bob of mass $$m$$. When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal the net force on the bob is:
  • $$\sqrt { 10 } mg$$
  • $$\sqrt { 5 } mg$$
  • $$4mg$$
  • $$1mg$$
Which of the following statements is incorrect?
  • Kinetic energy may be zero, positive or negative
  • Power, energy and work are all scalars
  • Potential energy may be zero, positive or negative
  • Ballistic pendulum is a device for measuring the speed of bullets
When a rubber-band is stretched by a distance $$x$$, it exerts a restoring force of magnitude $$F=ax+b{x}^{2}$$ where $$a$$ and $$b$$ are constants.The work done in stretching the unstretched rubber band by $$L$$ is:
  • $$\cfrac { a{ L }^{ 2 } }{ 2 } +\cfrac { { bL }^{ 3 } }{ 3} $$
  • $$\cfrac { 1 }{ 2 } \left( \cfrac { a{ L }^{ 2 } }{ 2 } +\cfrac { { bL }^{ 3 } }{ 2 } \right) $$
  • $$a{ L }^{ 2 }+{ bL }^{ 3 }$$
  • $$\cfrac { 1 }{ 2 } \left( a{ L }^{ 2 }+{ bL }^{ 3 } \right) $$
Which of the following is not an example of potential energy?
  • A vibrating pendulum at its maximum displacement from the mean position
  • A body at rest at some height from the ground
  • A wound clock-spring
  • A vibrating pendulum when it is just passing through the mean position
A body of mass $$0.5\ kg$$ travels in a straight line with velocity $$v = ax^{1/2}$$ where $$a = 4 m^{}s^{-2}$$. The work done by the net force during its displacement from $$x = 0$$ to $$x = 2\ m$$ is
  • $$1.5\ J$$
  • $$50\ J$$
  • $$10\ J$$
  • None of these
A force $$F$$ acting on an object varies with distance $$x$$ as shown in the figure. The work done by the force in moving the object from $$x = 0$$ and $$x = 20\ m$$ is
939454_d43728c9b08c46d79a464ab03995b066.png
  • $$500\ J$$
  • $$1000\ J$$
  • $$1500\ J$$
  • $$2000\ J$$
When spring is cut into parts its effective spring constant of each part decreases.
State whether True/False?
  • True
  • False
A body of mass starts moving from rest along x-axis so that its velocity varies as $$v = a\sqrt {s}$$ where $$a$$ is a constant and $$s$$ is the distance covered by the body. The total work done by all the forces acting on the body in the first seconds after the start of the motion is:
  • $$\dfrac {1}{8} ma^{4}t^{2}$$
  • $$4\ ma^{4}t^{2}$$
  • $$8 ma^{4}t^{2}$$
  • $$\dfrac {1}{4}ma^{4}t^{2}$$
A body of mass $$0.5\ kg$$ travels in a straight line with velocity $$v = ax^{3/2}$$ where $$a = 5\ m^{-1/2}s^{-1}$$. The work done by the net force during its displacement from $$x = 0$$ to $$x = 2m$$ is
  • $$1.5\ J$$
  • $$50\ J$$
  • $$10\ J$$
  • $$100\ J$$
A man revolves a stone of mass m tied to the end of a string in a vertical circle of radius R, The net force at the lowest and height points of the circle directed vertical downwards are 
Here $$T_1, T_2$$ and  $$v_1, v_2$$ denote the tension in the string and the speed of the stone at the lowest and highest points, respectively.
  • Lowest point: $$mg - T_1$$ Highest point : $$mg + T_2$$
  • Lowest point: $$mg + T_1$$ Highest point : $$mg - T_2$$
  • Lowest point: $$mg + T_1 -\frac{mv^2}{R}$$ Highest point: $$mg - T_2 +\frac{mv^2}{r}$$
  • Lowest point: $$mg - T_1 -\frac{mv^2}{R}$$ Highest point: $$mg + T +\frac{mv^2}{r}$$
A force F is related to the position of a particle by the relation $$ F =(10x^2)N$$. The work done by the force when the particle moves from x=2m to x=4 m is
  • $$\dfrac{56}{3}J$$
  • $$560 J$$
  • $$\dfrac {560}{3}J$$
  • $$\dfrac{3}{560} J$$
Two wires $$AC$$ and $$BC$$ are tied at $$C$$ of a small sphere of mass $$5\ kg$$, which revolves at a constant speed $$v$$ in the horizontal plane with the speed $$v$$ of radius $$1.6\ m$$. Find the minimum value of $$v$$.
987320_03c2ec504f0f40f49da1331d19c90e9a.png
  • $$4\ m{s}^{-1}$$
  • $$2\ m{s}^{-1}$$
  • $$2.5\ m{s}^{-1}$$
  • None of these
The velocity of a body moving in a vertical circle of radius r is $$\sqrt{7gr}$$ at the lowest point of the circle. What is the ratio of maximum and minimum tension?
  • $$4: 1$$
  • $$\sqrt 7:1$$
  • $$3: 1$$
  • $$2: 1$$
two blocks of masses $$m_1 = 2 kg$$ and $$m_2 = 4 kg$$ are moving in the same direction with speeds $$\nu_1 = 6 m/s$$ and $$\nu_2 = 3 m/s$$, respectively on a frictioneless surface as shown in the figure. An ideal spring with spring constant $$k = 30000 N/m$$ is attached to the back side of $$m_2$$. Then the maximum compression of the spring after collision will be:
995757_f2462dc967a44c39b7979823e77459e7.png
  • $$0.06 m$$
  • $$0.04 m$$
  • $$0.02 m$$
  • none of these
A particle of mass 1 kg is suspended by means of a string of length L=2 m. The string makes $$6/\pi$$ rps around a vertical axis through the fixed end. The tension in the string is
  • 72 N
  • 36 N
  • 288 N
  • 10 N
A 0.25kg ball attached to a 1.5 m rope moves with a constant speed of 15 m/s around a vertical circle. Calculate the tension force on the rope at the middle of the circle:
  • 37.5 N
  • 137.5 N
  • 2.5 N
  • 25 N
A mass attached to a string that is itself attached to the ceiling swings back and forth. If the bob is observed to be moving upward at a given instance, as shown to the right, which arrow best depicts the direction of the net force acting on the bob at that instant
1004868_45bb52a2d04041709d1dadbd2a9924ad.PNG
  • A
  • B
  • C
  • D
A time-varying force $$F=6t-2{ t }^{ 2 } N$$, at $$t=0$$ starts acting on a body of mass $$2 kg$$ initially at rest, where t is in second. The force is withdrawn just at the instant when the body comes to rest again. We can see that at $$t=0$$,the force $$F=0$$. Now answer the following:
Mark the correct statement:
  • Velocity of the body is maximum when force acting on the body is maximum for the first time.
  • The velocity of the body becomes maximum when force acting on the body becomes zero again
  • When force becomes zero again, velocity of the body also becomes zero at that instant.
  • All of the avove
A force $$F = -K(x\hat {i} + y\hat {j})$$ (where $$K$$ is a positive constant) acts on a particle moving in the $$x-y$$ plane. Starting from the origin, the particle is taken along the positive $$x-$$ axis to the point $$(a, 0)$$ and then to the point $$(a, a)$$. The total work done by the force $$\vec {F}$$ on the particle is
  • $$-2Ka^{2}$$
  • $$2Ka^{2}$$
  • $$-Ka^{2}$$
  • $$Ka^{2}$$
A spring of spring constant $$5\times {10}^{3}N/m$$ is stretched initially by $$5cm$$ from unstretched position. Then the work required to stretch is further by another $$5cm$$ is then
  • $$12.50N-m$$
  • $$18.75N-m$$
  • $$25.00N-m$$
  • $$6.25N-m$$
A mass of $$M\ kg$$ is suspended by a weightless string. The horizontal force that is required to displace it unitl the string makes an angle of $${45}^{o}$$ with the initial vertical direction is
  • $$Mg(\sqrt{2}-1)$$
  • $$Mg(\sqrt{2}+1)$$
  • $$Mg\sqrt {2}$$
  • $$\cfrac { Mg }{ \sqrt { 2 } } $$
A thin uniform rod of mass $$m$$ and length $$l$$ is hinged at the lower end of a level floor and stands vertically. It is now allowed to fall, then its upper and will strike the floor with a velocity given by(A)$$\sqrt { mgl }$$(B) $$\sqrt { 3gl }$$(c)$$\sqrt { 5gl }$$ (D) $$\sqrt { 2gl }$$  Sol. 
  • A
  • B
  • C
  • D
In an elastic collision between two particles
  • net kinetic force is zero
  • the kinetic energy of the system before collision is equal to the kinetic of the system after collision
  • linear momentum of system before collision = linear momentum after collision
  • the total energy of the system is never conserved
The work done by a force is equal to :

  • the area under $$f\left( x \right) $$ vs $$x$$ curve and $$x$$ axis
  • half the area under $$f\left( x \right) $$ vs $$x$$ curve and $$x$$ axis
  • the area under $$f\left( x \right) $$ vs $$x$$ curve and $$F$$ axis
  • half the area under $$f\left( x \right) $$ vs $$x$$ curve and $$F$$ axis
When a rubber-bank is stretched by a distance $$x$$, it exerts a restoring force of magnitude $$F=ax+b{x}^{2}$$ where $$a$$ and $$b$$ are constants. The work done in stretching the unstretched rubber band by $$L$$ is:
  • $$\cfrac { a{ L }^{ 2 } }{ 2 } +\cfrac { b{ L }^{ 3 } }{ 3 } $$
  • $$\cfrac { 1 }{ 2 } \left( \cfrac { a{ L }^{ 2 } }{ 2 } +\cfrac { b{ L }^{ 3 } }{ 3 } \right) $$
  • $$a{ L }^{ 2 }+b{ L }^{ 3 }$$
  • $$\cfrac { 1 }{ 2 } \left( a{ L }^{ 2 }+b{ L }^{ 3 } \right) $$
A particle moves along $$X-$$axis from $$x=0$$ to $$x=1\ m$$ under the influence of a force given by $$F=3x^{2}+2x-10$$. Work done in the process is:
  • $$+4\ J$$
  • $$-4\ J$$
  • $$+8\ J$$
  • $$-8\ J$$
A body of mass $$1kg$$ thrown upwards with a velocity of $$10m/s$$ comes to rest (momentarily) after moving up by $$4m$$. The work done by air drag in this process is (Take $$g=10m/{ s }^{ 2 }$$)
  • $$-20J$$
  • $$-10J$$
  • $$-30J$$
  • $$0J$$
$$4\ J$$ of work is required to stretch a spring through $$10\ cm$$ beyond its unstreched length. The extra work required to stretch it through additional $$10\ cm$$ shall be
  • $$4\ J$$
  • $$8\ J$$
  • $$12\ J$$
  • $$16\ J$$
A particle moves along $$y=\sqrt { 1-{ x }^{ 2 } } $$ betweem the points $$(0,-1)m$$ and $$(0,1)m$$ under the influence of a force $$\overrightarrow { F } =\left( { y }^{ 2 }\hat { i } +{ x }^{ 2 }\hat { j }  \right) N$$. Then
  • the particle is moving along a semi-ellipse
  • the particle is moving along a semicircle
  • work done on the particle by $$\overrightarrow { F } $$ is $$(3/4)J$$
  • work done on the particle by $$\overrightarrow { F } $$ is $$(4/3)J$$
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