JEE Main & Advanced Physics Two Dimensional Motion Question Bank

done Critical Thinking Total Questions - 17

• question_answer1)
  A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that                                 [IIT 1987]
  A)
              Velocity is constant done clear
  B)
              Acceleration is constant done clear
  C)
              Kinetic energy is constant done clear
  D)
              It moves in a circular path   done clear
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• question_answer2)
  A tube of length \[L\] is filled completely with an incompressible liquid of mass \[M\] and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity \[\omega \]. The force exerted by the liquid at the other end is   [IIT 1992]
  A)
              \[\frac{ML{{\omega }^{2}}}{2}\] done clear
  B)
                \[ML{{\omega }^{2}}\] done clear
  C)
              \[\frac{ML{{\omega }^{2}}}{4}\]   done clear
  D)
              \[\frac{M{{L}^{2}}{{\omega }^{2}}}{2}\]   done clear
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• question_answer3)
  The kinetic energy \[k\] of a particle moving along a circle of radius \[R\] depends on the distance covered \[s\] as \[k=a{{s}^{2}}\] where \[a\] is a constant. The force acting on the particle is [MNR 1992; JIPMER 2001, 02; AMU (Engg.) 1999]
  A)
              \[2a\frac{{{s}^{2}}}{R}\]   done clear
  B)
    \[2as{{\left( 1+\frac{{{s}^{2}}}{{{R}^{2}}} \right)}^{1/2}}\] done clear
  C)
              \[2as\]  done clear
  D)
              \[2a\frac{{{R}^{2}}}{s}\]   done clear
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• question_answer4)
  A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track is [IIT 1992]
  A)
              Zero     done clear
  B)
              \[{{30}^{o}}\] done clear
  C)
              \[{{45}^{o}}\]          done clear
  D)
              \[{{60}^{o}}\] done clear
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• question_answer5)
  A particle of mass \[m\] is moving in a circular path of constant radius \[r\] such that its centripetal acceleration \[{{a}_{c}}\] is varying with time t as, \[{{a}_{c}}={{k}^{2}}r{{t}^{2}}\], The power delivered to the particle by the forces acting on it is                  [IIT 1994]
  A)
              \[2\pi m{{k}^{2}}{{r}^{2}}t\] done clear
  B)
                \[m{{k}^{2}}{{r}^{2}}t\] done clear
  C)
              \[\frac{m{{k}^{4}}{{r}^{2}}{{t}^{5}}}{3}\] done clear
  D)
                Zero done clear
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• question_answer6)
  A string of length L is fixed at one end and carries a mass M at the other end.  The string makes 2/p revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is [BHU 2002; DPMT 2004]
  A)
              ML       done clear
  B)
              2 ML done clear
  C)
              4 ML    done clear
  D)
              16 ML done clear
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• question_answer7)
  A stone of mass 1 kg tied to a light inextensible string of length \[L=\frac{10}{3}m\] 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 in the string is 4 and if \[g\] is taken to be \[10m/{{\sec }^{2}}\], the speed of the stone at the highest point of the circle is                                 [CBSE PMT 1990]
  A)
              \[20m/\sec \] done clear
  B)
                \[10\sqrt{3}m/\sec \] done clear
  C)
              \[5\sqrt{2}\,m/\sec \] done clear
  D)
                \[10m/\sec \] done clear
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• question_answer8)
  A particle \[P\] is sliding down a frictionless hemispherical bowl. It passes the point  \[A\] at \[t=0\]. At this instant of time, the horizontal component of its velocity is \[v\]. A bead \[Q\] of the same mass as \[P\] is ejected from \[A\] at \[t=0\] along the horizontal string \[AB\] (see figure) with the speed \[v\]. Friction between the bead and the string may be neglected. Let \[{{t}_{P}}\] and \[{{t}_{Q}}\] be the respective time taken by \[P\] and \[Q\] to reach the point \[B\]. Then                               [IIT 1993]   
  A)
              \[{{t}_{P}}<{{t}_{Q}}\] done clear
  B)
                \[{{t}_{P}}={{t}_{Q}}\] done clear
  C)
              \[{{t}_{P}}>{{t}_{Q}}\] done clear
  D)
                All of these done clear
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• question_answer9)
  A long horizontal rod has a bead which can slide along its length, and initially placed at a distance L from one end A of the rod.  The rod is set in angular motion about A with constant angular acceleration a. If the coefficient of friction between the rod and the bead is m, and gravity is neglected, then the time after which the bead starts slipping is                                              [IIT-JEE Screening 2000]
  A)
              \[\sqrt{\frac{\mu }{\alpha }}\] done clear
  B)
              \[\frac{\mu }{\sqrt{\alpha }}\] done clear
  C)
              \[\frac{1}{\sqrt{\mu \alpha }}\]          done clear
  D)
              Infinitesimal done clear
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• question_answer10)
  A small block is shot into each of the four tracks as shown below.  Each of the tracks rises to the same height.  The speed with which the block enters the track is the same in all cases.  At the highest point of the track, the normal reaction is maximum in                                               [IIT-JEE Screening 2001]
  A)
                          done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
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• question_answer11)
  A simple pendulum is oscillating without damping.  When the displacement of the bob is less than maximum, its acceleration vector \[\vec{a}\] is correctly shown in             [IIT-JEE Screening 2002]
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
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• question_answer12)
  A solid disc rolls clockwise without slipping over a horizontal path with a constant speed \[\upsilon \].  Then the magnitude of the velocities of points A, B and C (see figure) with respect to a standing observer are respectively [UPSEAT 2002]
  A)
               \[\upsilon ,\,\upsilon \text{ and }\upsilon \] done clear
  B)
                \[2\upsilon ,\,\sqrt{2}\upsilon \text{ and}\,\text{zero}\] done clear
  C)
              \[2\upsilon ,\,2\upsilon \text{ and}\,\text{zero}\] done clear
  D)
                \[2\upsilon ,\,\sqrt{2}\upsilon \text{ and}\,\sqrt{2}\upsilon \] done clear
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• question_answer13)
  A stone tied to a string of length \[L\] is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed \[u\]. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is    [IIT 1998; CBSE PMT 2004]
  A)
              \[\sqrt{{{u}^{2}}-2gL}\] done clear
  B)
                \[\sqrt{2gL}\] done clear
  C)
              \[\sqrt{{{u}^{2}}-gl}\] done clear
  D)
                \[\sqrt{2({{u}^{2}}-gL)}\] done clear
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• question_answer14)
  The driver of a car travelling at velocity v suddenly see a broad wall in front of him at a distance d. He should             [IIT 1977]
  A)
              Brake sharply done clear
  B)
                Turn sharply done clear
  C)
              (a) and (b) both           done clear
  D)
              None of the above done clear
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• question_answer15)
  Four persons \[K,\,L,\,M\] and \[N\] are initially at the corners of a square of side of length \[d\]. If every person starts moving, such that \[K\] is always headed towards \[L,\,L\] towards \[M,\,M\] is headed directly towards \[N\] and \[N\] towards\[K\], then the four persons will meet after                            [IIT 1984]
  A)
              \[\frac{d}{v}\] sec done clear
  B)
                \[\frac{\sqrt{2d}}{v}\] sec done clear
  C)
              \[\frac{d}{\sqrt{2v}}\] sec done clear
  D)
                \[\frac{d}{2v}\] sec done clear
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• question_answer16)
  The coordinates of a particle moving in a plane are given by \[=-\ 8\ m/{{s}^{2}}.\] and \[y(t)=b\sin (pt)\] where \[a,\,\,b\,(<a)\] and \[p\] are positive constants of appropriate dimensions. Then                                      [IIT-JEE 1999]
  A)
              The path of the particle is an ellipse done clear
  B)
              The velocity and acceleration of the particle are normal to each other at \[t=\pi /(2p)\] done clear
  C)
              The acceleration of the particle is always directed towards a focus done clear
  D)
              The distance travelled by the particle in time interval \[t=0\] to \[t=\pi /(2p)\] is \[a\] done clear
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• question_answer17)
  A particle is moving eastwards with velocity of 5 m/s. In 10 sec the velocity changes to 5 m/s northwards. The average acceleration in this time is      [IIT 1982; AFMC 1999; Pb PET 2000; JIPMER 2001, 02]
  A)
              Zero done clear
  B)
              \[\frac{1}{\sqrt{2}}\,\,m\text{/}{{s}^{\text{2}}}\] toward north-west done clear
  C)
              \[\frac{1}{\sqrt{2}}\,\,m\text{/}{{s}^{\text{2}}}\] toward north-east done clear
  D)
              \[\frac{1}{2}\,\,m\text{/}{{s}^{\text{2}}}\]toward north-west done clear
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