JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank

done Mock Test - Gravitation and Mechanical Properties of Solid Total Questions - 25

• question_answer1)
  A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energy is
  A)
  Positive done clear
  B)
   Negative done clear
  C)
   Zero done clear
  D)
   May be positive or negative depending upon its initial velocity done clear
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• question_answer2)
  A rocket of mass \[M\] is launched vertically from the surface of the earth with an initial speed \[V\] Assuming the radius of the earth to be \[R\] and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
  A)
  \[R/\left( \frac{gR}{2{{V}^{2}}}-1 \right)\]                      done clear
  B)
  \[{{R}_{{}}}\left( \frac{gR}{2{{V}^{2}}}-1 \right)\] done clear
  C)
  \[R/\left( \frac{gR}{2{{V}^{2}}}-1 \right)\]         done clear
  D)
  \[R\left( \frac{2gR}{{{V}^{2}}}-1 \right)\] done clear
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• question_answer3)
  Suppose, the acceleration due to gravity at the Earth's surface is \[10\,m{{s}^{2}}\] and at the surface of Mars it is \[4.0\,m/{{s}^{2}}\].\[A\,60-kg\] passenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of figure best represents the weight (net gravitational force) of the passenger as a function of time?
  A)
  A                      done clear
  B)
  B done clear
  C)
  C         done clear
  D)
  D done clear
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• question_answer4)
  The earth moves around the Sun in an elliptical orbit as shown Earth in the figure. The ratio\[OA/OB=x\]. The ratio of the speed of the earth at B to that at A is nearly
  A)
  \[\sqrt{x}\]                    done clear
  B)
  \[x\] done clear
  C)
  \[x\sqrt{x}\]      done clear
  D)
  \[{{x}^{2}}\] done clear
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• question_answer5)
  As observed from the earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from the earth, this would
  A)
  be similarly true done clear
  B)
   not be true because the force between the earth and mercury is not inverse square law done clear
  C)
   not be true because the major gravitational force on mercury is due to the sun done clear
  D)
   not be true because mercury is influenced by forces other than gravitational forces done clear
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• question_answer6)
  A rubber of volume 2000 cc is alternately subjected to tension and released. The figure shows the stress-strain curve of rubber. Each curve is a quadrant of an ellipse. The. amount of energy lost as heat per cycle per unit volume will be
  A)
   \[\left( \frac{\pi }{2}-1 \right)\times 16\times {{10}^{2}}J\]          done clear
  B)
  \[\left( \frac{\pi }{4}-1 \right)\times 8\times {{10}^{2}}J\] done clear
  C)
   \[\left( \frac{\pi }{4}-1 \right)\times 32\times {{10}^{2}}J\]          done clear
  D)
   \[\left( \frac{\pi }{2}-1 \right)\times 32\times {{10}^{2}}J\] done clear
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• question_answer7)
  Two wires are made of the same material and have the same volume. However, wire 1 has cross-sectional area \[A\] and wire 2 has cross-sectional area\[3A\]. If the length of wire 1 increases by Ax on applying a force \[F\], how much force is needed to stretch wire 2 by the same amount?
  A)
  \[F\]                                         done clear
  B)
   \[4F\] done clear
  C)
  \[6F\]                done clear
  D)
  \[9F\] done clear
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• question_answer8)
  If the radius of the earth decreases by 10%, the mass remaining unchanged, what will happen to the acceleration due to gravity?
  A)
  Decreases by 19% done clear
  B)
   Increases by 19% done clear
  C)
   Decreases by more than 19% done clear
  D)
   Increase by more than 19% done clear
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• question_answer9)
  Wires \[A\] and \[B\] are connected with blocks \[P\] and \[Q\], as shown. The ratio of lengths, radii and Young's modulus of wires \[A\] and \[B\] are \[r,\,2r\] and 3r respectively (\[r\] is a constant). Find the mass of block \[P\] if ratio of increase in their corresponding lengths is \[\frac{1}{6{{r}^{2}}}\]. The mass of the block \[Q\] is 3\[M\]
  A)
  \[M\]                done clear
  B)
  \[3M\] done clear
  C)
  \[6M\]               done clear
  D)
  \[9M\] done clear
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• question_answer10)
  The ratio of diameters of two wires of same material is n: 1. The length of each wire is 4 m. On applying the same load, the increases in the length of the thin wire will be (n>\)
  A)
  \[{{n}^{2}}times\]       done clear
  B)
  \[{{n}^{{}}}times\] done clear
  C)
  \[2{{n}^{{}}}times\]   done clear
  D)
  \[{{(2n+1)}^{{}}}times\] done clear
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• question_answer11)
  Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is 0.5 cm, the elongation (\[l\]) of each wireis\[{{Y}_{s}}(steel)=2.0\times {{10}^{11}}N/{{m}^{2}}\] \[{{Y}_{c}}(copper)=1.2\times {{10}^{11}}N/{{m}^{2}}\]
  A)
  \[{{l}_{s}}=0.75\,cm,\,{{l}_{c}}=1.25\,cm\] done clear
  B)
   \[{{l}_{s}}=1.25\,cm,\,{{l}_{c}}=0.75\,cm\] done clear
  C)
   \[{{l}_{s}}=0.25\,cm,\,{{l}_{c}}=0.75\,cm\] done clear
  D)
   \[{{l}_{s}}=0.75\,cm,\,{{l}_{c}}=0.25\,cm\] done clear
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• question_answer12)
  A rectangular block of size \[10cm\times 8cm\times 5cm\] is kept in three different positions P, Q and R in turn as shown in the figure. In each case, the shaded area is rigidly fixed and a definite force F is applied tangentially to the opposite face to deform the block. The displacement of the upper face will be
  A)
  Same in all the three cases done clear
  B)
   Maximum in \[P\] position done clear
  C)
   Maximum in \[Q\] position done clear
  D)
   Maximum in \[R\] position done clear
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• question_answer13)
  The length of an elastic string is \[a\] metre when the longitudinal tension is 4 N and \[b\] metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is
  A)
  \[a-b\]   done clear
  B)
  \[5b-4a\] done clear
  C)
  \[2a-\frac{1}{4}a\]        done clear
  D)
  \[4a-3b\] done clear
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• question_answer14)
  A uniform ring of mass \[m\] and radius r is placed directly above a uniform sphere of mass \[M\] and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance \[r\sqrt{3}\]\[r\] as shown in the figure. The gravitational force exerted by the sphere on the ring will be
  A)
  \[\frac{GMm}{8{{r}^{2}}}\]    done clear
  B)
  \[\frac{GMm}{4{{r}^{2}}}\] done clear
  C)
  \[\sqrt{3}\frac{GMm}{8{{r}^{2}}}\]    done clear
  D)
  \[\frac{GMm}{8{{r}^{2}}\sqrt{3}}\] done clear
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• question_answer15)
  In a cosmic event, suppose a planet heavier than the earth with mass KM (K > 1) and radius K'R (K > 1) passes through a path near the earth (M and R are the mass and radius of earth). At what closest distance from surface of planet, we are in danger of  being thrown into space:
  A)
   \[{{\left[ \frac{2KGM}{g} \right]}^{1/2}}-\frac{1}{2}K'R\] done clear
  B)
   \[{{\left[ \frac{KGM}{2g} \right]}^{1/2}}-\frac{1}{2}K'R\] done clear
  C)
   \[{{\left[ \frac{KGM}{g} \right]}^{1/2}}-\frac{1}{2}K'R\] done clear
  D)
   \[{{\left[ \frac{KGM}{g} \right]}^{1/2}}-K'R\] done clear
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• question_answer16)
  Two planets revolve with same angular velocity about a star. The radius of orbit of outer planet is twice the radius of orbit of the inner planet. If Tis time period of the revolution of outer planet, find the time in which inner planet will fall into the star. If it was suddenly stopped.
  A)
  \[\frac{T\sqrt{2}}{8}\]   done clear
  B)
  \[\frac{T\sqrt{2}}{16}\] done clear
  C)
  \[\frac{T\sqrt{2}}{4}\]   done clear
  D)
  \[\frac{T\sqrt{2}}{32}\] done clear
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• question_answer17)
   A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed (\[{{v}_{0}}\]). Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If \[R\]= radius of the Earth and \[\omega \]) be its angular speed of the Earth about its own axis. Then find the approximate difference in the two time period as observed on the Earth.
  A)
  \[\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\]        done clear
  B)
  \[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\] done clear
  C)
  \[\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\]         done clear
  D)
  \[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\] done clear
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• question_answer18)
  Four particles, each of mass \[M\]and equidistant from each other, move along a circle of radius \[R\] under the action of their mutual gravitational attraction. The speed of each particle is
  A)
  \[\sqrt{\frac{GM}{R}(1+2\sqrt{2})}\] done clear
  B)
  \[\frac{1}{2}\sqrt{\frac{GM}{R}(1+2\sqrt{2})}\] done clear
  C)
  \[\sqrt{\frac{GM}{R}}\]             done clear
  D)
  \[\sqrt{2\sqrt{2}\frac{GM}{R}}\] done clear
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• question_answer19)
  If \[{{W}_{1}}\], \[{{W}_{2}}\] and \[{{W}_{3}}\] represent the work done in moving a particle from A to B along three different paths 1, 2 and 3, respectively, (as shown in the figure) in the gravitational field of a point mass m, find the correct relation between \[{{W}_{1}}\],\[{{W}_{2}}\] and \[{{W}_{3}}\].
  A)
  \[{{W}_{1}}>{{W}_{2}}>{{W}_{3}}\] done clear
  B)
  \[{{W}_{1}}={{W}_{2}}={{W}_{3}}\] done clear
  C)
  \[{{W}_{1}}<{{W}_{2}}<{{W}_{3}}\] done clear
  D)
  \[{{W}_{2}}<{{W}_{1}}<{{W}_{3}}\] done clear
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• question_answer20)
  Two bodies of masses \[{{M}_{1}}\] and \[{{M}_{2}}\] are placed at a distance \[R\]apart. Then at the position where the gravitational field due to them is zero, the gravitational potential is
  A)
  \[-G\frac{\sqrt{{{M}_{1}}}}{R}\]          done clear
  B)
  \[-G\frac{\sqrt{{{M}_{2}}}}{R}\] done clear
  C)
  \[-{{(\sqrt{{{M}_{1}}}+\sqrt{{{M}_{2}}})}^{2}}\frac{G}{R}\]            done clear
  D)
  \[-{{(\sqrt{{{M}_{1}}}-\sqrt{{{M}_{2}}})}^{2}}\frac{G}{R}\] done clear
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• question_answer21)
  A wire is suspended vertically. One of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire (in Joule) is _______ .
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• question_answer22)
  Two rods of different materials having coefficients of linear expansion \[{{a}_{1}}\] and \[{{a}_{2}}\]and Young's moduli, \[{{Y}_{1}}\]and\[{{Y}_{2}}\], respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If \[{{a}_{1}}/{{a}_{2}}=2/3\], then the thermal stresses developed in the two rods are equal, provided \[{{Y}_{1}}/{{Y}_{2}}\] is equal to_______ .
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• question_answer23)
  Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is\[(40/3\pi )\times {{10}^{6}}N/{{m}^{2}}\]. If\[g=10m{{s}^{-12}}\], then what should be the minimum radius (in mm) of the wire used if it is not to break?
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• question_answer24)
  The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by\[{{100}^{0}}C\,(in\times {{10}^{8}}pa)\]is ______. (For steel Young's modulus is \[2\times {{10}^{11}}N{{m}^{-2}}\] and coefficient of thermal expansion is \[1.1\times {{10}^{-5}}{{K}^{-1}}\])
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• question_answer25)
  Two spherical bodies of masses \[m\] and \[5M\]and radii \[R\] and 2\[R\], respectively, are released in free space with initial separation between their centres equal to 12R. If they attract each other by gravitational force only, then the distance covered by the smaller body just before collision is __R.
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