JEE Main & Advanced Physics Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति Question Bank

done Mock Test - Work Power and Energy Total Questions - 25

• question_answer1)
  A spring is compressed between two toy carts of masses \[{{m}_{1}}\]and\[{{m}_{2}}\]. When the toy carts are released, the spring exerts on each toy cart equal and opposite forces for the same small time \[t\]. If the coefficients of friction \[\mu \] between the ground and the toy carts are equal, then the magnitude of displacements of the toy carts are in the ratio
  A)
  \[\frac{{{S}_{1}}}{{{S}_{2}}}=\frac{{{m}_{2}}}{{{m}_{2}}}\]        done clear
  B)
  \[\frac{{{S}_{1}}}{{{S}_{2}}}=\frac{{{m}_{1}}}{{{m}_{2}}}\] done clear
  C)
  \[\frac{{{S}_{1}}}{{{S}_{2}}}={{\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)}^{2}}\] done clear
  D)
  \[\frac{{{S}_{1}}}{{{S}_{2}}}={{\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)}^{2}}\] done clear
  View Solution play_arrow

• question_answer2)
  A particle of mass \[m\] moves with a variable velocity \[v\], which changes with distance covered \[x\] along a straight line as \[v=k\sqrt{x}\], where A: is a positive constant. The work done by all the forces acting on the particle, during the first \[t\] seconds is
  A)
  \[\frac{m{{k}^{4}}}{{{t}^{2}}}\] done clear
  B)
  \[\frac{m{{k}^{4}}{{t}^{2}}}{4}\] done clear
  C)
  \[\frac{m{{k}^{4}}{{t}^{2}}}{8}\] done clear
  D)
  \[\frac{m{{k}^{4}}{{t}^{2}}}{16}\] done clear
  View Solution play_arrow

• question_answer3)
  A projectile is fired with some velocity making certain angle with the horizontal. Which of the following graphs is the best representation for the kinetic energy of a projectile (KE) versus its horizontal displacement (x)?
  A)
  done clear
  B)
    done clear
  C)
  done clear
  D)
    done clear
  View Solution play_arrow

• question_answer4)
  Figure shows a plot of the conservative force F in a unidimensional field. The plot representing the function corresponding to the potential energy (U) m the field is.
  A)
    done clear
  B)
    done clear
  C)
    done clear
  D)
    done clear
  View Solution play_arrow

• question_answer5)
  A mass m starting from A reaches B of a frictionless track. On reaching B, it pushes the track with a force equal to x times its weight, then the applicable relation is
  A)
   \[h=\frac{(x+5)}{2}r\]              done clear
  B)
   \[h=\frac{x}{2}r\] done clear
  C)
   \[h=r\]              done clear
  D)
   \[h=\left( \frac{x+1}{2} \right)r\] done clear
  View Solution play_arrow

• question_answer6)
  A particle of mass m moves along a circular path of radius r with centripetal acceleration \[{{a}_{n}}\] changing with time t as \[{{a}_{n}}=k{{t}^{2}}\], where k is-a positive constant. The average power developed by all the forces acting on the particle during the first \[{{t}_{0}}\] seconds is
  A)
  \[mkr{{t}_{0}}\] done clear
  B)
  \[\frac{mkr{{t}_{0}}^{2}}{2}\] done clear
  C)
  \[\frac{mkr{{t}_{0}}^{{}}}{2}\]                      done clear
  D)
  \[\frac{mkr{{t}_{0}}^{{}}}{4}\] done clear
  View Solution play_arrow

• question_answer7)
  A simple pendulum consisting of a mass \[M\] attached to a string of length L is released from rest at an angle \[a\]. A pin is located at a distance \[l\] below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. The maximum angle \[\theta \] which the string makes with the vertical after hitting the pin is
  A)
   \[{{\cos }^{1}}\left[ \frac{L\,\cos a+l}{L+l} \right]\]      done clear
  B)
   \[{{\cos }^{1}}\left[ \frac{L\,\cos a+l}{L-l} \right]\] done clear
  C)
   \[{{\cos }^{1}}\left[ \frac{L\,\cos a-l}{L-l} \right]\]          done clear
  D)
   \[{{\cos }^{1}}\left[ \frac{L\,\cos a-l}{L+l} \right]\] done clear
  View Solution play_arrow

• question_answer8)
  A heavy particle hanging from a string of length \[l\]is projected horizontally with speed \[\sqrt{2gl}\]. The speed of the particle at the point where the tension in the string equals weight of the particle
  A)
  \[\sqrt{2gl}\]      done clear
  B)
  \[\sqrt{3gl}\] done clear
  C)
  \[\sqrt{gl/2}\]     done clear
  D)
  \[\sqrt{gl/3}\] done clear
  View Solution play_arrow

• question_answer9)
  A particle is moving in the vertical plane. It is attached at one end of a string of length \[\lambda \] whose other end is fixed. The velocity at the lowest point is \[u\]. The tension in the string is \[\vec{T}\] and velocity of the particle is \[\vec{v}\] at any position. Then, which of the following quantity will remain constant.
  A)
   \[\vec{T}.\vec{v}\] done clear
  B)
   kinetic energy done clear
  C)
   Gravitational potential energy done clear
  D)
   \[\vec{T}\times \vec{v}\] done clear
  View Solution play_arrow

• question_answer10)
  The kinetic energy of a particle moving along a straight line increases uniformly with respect to the distance travelled by it. The force acting on the particle is (\[v\] is the speed of particle at any time)
  A)
  constant done clear
  B)
  proportional to \[v\] done clear
  C)
  proportional to \[{{v}^{2}}\] done clear
  D)
  inversely proportional to \[v\] done clear
  View Solution play_arrow

• question_answer11)
  Blocks \[A\] and \[B\] of mass m each are connected with spring of constant \[k\]. Both blocks lie on frictionless ground and are imparted horizontal velocity v as shown when spring is unstretched. Find the maximum stretch of spring.
  A)
  \[v\sqrt{\frac{m}{k}}\]  done clear
  B)
  \[v\sqrt{\frac{m}{2k}}\] done clear
  C)
  \[v\sqrt{\frac{2m}{k}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  Find the maximum compression in the spring, if the lower block is shifted to rightwards with Acceleration \['a'\] All the surfaces are smooth:
  A)
  \[\frac{ma}{2k}\]                      done clear
  B)
  \[\frac{2ma}{k}\] done clear
  C)
  \[\frac{ma}{k}\]                        done clear
  D)
  \[\frac{4ma}{k}\] done clear
  View Solution play_arrow

• question_answer13)
  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,
  A)
  \[\frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3}\]        done clear
  B)
  \[\frac{1}{2}\left( \frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3} \right)\] done clear
  C)
  \[a{{L}^{2}}+b{{L}^{3}}\]              done clear
  D)
  \[\frac{1}{2}(a{{L}^{2}}+a{{L}^{3}})\] done clear
  View Solution play_arrow

• question_answer14)
  A person trying to lose weight by burning fat lifts a mass of 10 kg up to a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies \[3.8\times {{10}^{7}}\] J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take \[g=9.8m{{s}^{-2}}\].
  A)
  \[2.45\times {{10}^{-3}}kg\] done clear
  B)
  \[6.45\times {{10}^{-3}}kg\] done clear
  C)
  \[9.89\times {{10}^{-3}}kg\] done clear
  D)
  \[12.89\times {{10}^{-3}}kg\] done clear
  View Solution play_arrow

• question_answer15)
  The block of mass \[M\] moving on a frictionless   horizontal   surface collides with a spring of spring constant \[k\] and compresses it by length \[L\]. The maximum momentum of the block after collision is
  A)
  \[\frac{M{{L}^{2}}}{k}\]        done clear
  B)
  zero done clear
  C)
  \[\frac{k{{L}^{2}}}{2M}\]                  done clear
  D)
  \[\sqrt{Mk}L\] done clear
  View Solution play_arrow

• question_answer16)
  The force exerted by a compression device is given by \[F(x)=kx\,(x-l)\,for\,0\le x\le l\], where \[l\] is the maximum possible compression, \[x\] is the compression and is a constant. The work required to compress the device by a distance \[d\]will be maximum when:
  A)
  \[d=\frac{l}{4}\]          done clear
  B)
  \[d=\frac{l}{\sqrt{2}}\] done clear
  C)
  \[d=\frac{l}{2}\]          done clear
  D)
  \[d=l\] done clear
  View Solution play_arrow

• question_answer17)
  A particle is released from the top of two inclined rough surfaces of height '\[h\]' each. The angle of inclination of the two planes are \[30{}^\circ \] and \[60{}^\circ \] respectively. All other factors (e.g. coefficient of friction, mass of block etc.) are same in both the cases. Let \[{{K}_{1}}\] and \[{{K}_{2}}\] be the kinetic energies of the particle at the bottom of the plane in two cases. Then
  A)
   \[{{K}_{1}}={{K}_{2}}\]                    done clear
  B)
   \[{{K}_{1}}>{{K}_{2}}\] done clear
  C)
   \[{{K}_{1}}<{{K}_{2}}\]        done clear
  D)
   data insufficient done clear
  View Solution play_arrow

• question_answer18)
  A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in the figure. If it starts its journey from rest at \[x=0\], its velocity at \[x=12\] m is
  A)
  \[0\,m/s\]          done clear
  B)
  \[20\sqrt{2}m/s\] done clear
  C)
  \[20\sqrt{3}m/s\]           done clear
  D)
  \[40\,m/s\] done clear
  View Solution play_arrow

• question_answer19)
  When a person stands on a weighing balance, workingon the principle of Hooke's law, it shows a reading of 60 kg after a long time and the spring gets compressed by2.5 cm. If the person jumps on the balance from a height of 10 cm, the maximum reading of the balance will be
  A)
  60 kg     done clear
  B)
  120kg done clear
  C)
  180 kg done clear
  D)
  240kg done clear
  View Solution play_arrow

• question_answer20)
  A particle located in a one-dimensional potential field has its potential energy function as \[U(x)\,\frac{a}{{{x}^{4}}}-\frac{b}{{{x}^{2}}}\], where a and b are positive constants. The position of equilibrium x corresponds to
  A)
  \[\frac{b}{2a}\]             done clear
  B)
  \[\sqrt{\frac{2a}{b}}\] done clear
  C)
  \[\sqrt{\frac{2a}{a}}\]   done clear
  D)
  \[\frac{a}{2a}\] done clear
  View Solution play_arrow

• question_answer21)
  A bead of mass 1/2 kg starts from rest from \[A\] to move in a vertical plane along a smooth fixed quarter ring of radius 5 m, under the action of a constant horizontal force F = 5 N as shown in the figure. The speed of bead as it reaches point \[B\] is _____ m/s.
  View Solution play_arrow

• question_answer22)
  A stone of mass 1 kg tied to a light inextensible string of length \[L=10/3\] m is whirling in a circular path of radius\[L\] in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension is 4 and g is taken to be \[10m{{s}^{-2}}\], the speed of the stone at the highest point of the circle is _____ m/s.
  View Solution play_arrow

• question_answer23)
  A ball weighing 1.0 kg is tied to a string 15 cm long. Initially the ball is held in position such that the string is horizontal. The ball is now released. A nail N is situated vertically below the support at a distance \[L\]. What is the minimum value of \[L\] (in cm) such that the string will be wound round the nail?
  View Solution play_arrow

• question_answer24)
  A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes an uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by (in cm) _____ .
  View Solution play_arrow

• question_answer25)
  An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that the efficiency of the engine is 60%, what is the power of the engine in (kW)? Take \[g=10m{{s}^{-2}}\].
  View Solution play_arrow