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question_answer1) There block A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an initial speed v towards B due to which it collides with B perfectly in elastically. The combined mass collides with C, also perfectly in elastically and \[\frac{5}{6}\]th of the initial kinetic energy is lost in whole process. If the value of M/m is\[\frac{4}{x}\]. Find the value of x.
question_answer2) A force acts on a 2 kg object so that its position is given as a function of time as \[x=3{{t}^{2}}+5.\] What is the work done (in joule) by this force in first 5 seconds?
question_answer3) A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity \[100\text{ }m{{s}^{-1}}\], from the ground. The bullet gets embedded in the wood. Then the maximum height (in metre) to which the combined system reaches above the top of the building before falling below is: \[\left( g=10m{{s}^{-2}} \right)\]
question_answer4) A particle which is experiencing a force, given by \[\vec{F}=3\vec{i}-12\vec{j},\] undergoes a displacement of \[\vec{d}=4\vec{i}.\] If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy (in joule) at the end of the displacement?
question_answer5) A body of mass 1 kg falls freely from a height of 100m, on a platform of mass 3 kg which is mounted on a spring having spring constant \[k=1.25\times {{10}^{6}}N/m.\] The body sticks to the platform and the spring's maximum compression is found to be x cm. Given that \[g=10\text{ }m{{s}^{-2}}\], the value of x will be close to:
question_answer6) An alpha-particle of mass m suffers one-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is x m. Find the value of x.
question_answer7) A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy (in joule) of the particle after it has travelled 3 m is:
question_answer8) A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass (in kg) of the second body?
question_answer9) A body of mass 3 kg is under a constant force which causes a displacement s in metre in it, given by the relation \[s=\frac{1}{3}{{t}^{3}}\], where t is in second. Work done (in joule) by the force in 2 second is
question_answer10) A ball is dropped from a height of 100 m. After striking the earth, 20% of its energy is lost. To what height (in metre) the ball will rise?
question_answer11) A force of 5 N making an angle \[\theta \] with the horizontal, acting on an object displaces it by 0.4m along the horizontal direction. If the object gains kinetic energy of 1J, the horizontal component of the force (in newton) is
question_answer12) A motor of 100 H.P. moves a load with a uniform speed of 72 km/h. The forward thrust (in newton) applied by the engine of the car is
question_answer13) Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of 0.4 m/s. It collides head on with the second elastically, the second one similarly with the third and so on. The velocity (in m/s) of the last ball is
question_answer14) A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2:3. The smaller fragment moves with a velocity of 6 m/s. The kinetic energy (in joule) of the larger fragment is
question_answer15) A ball drops from a celling of a room and after rebounding twice from the floor reaches a height equal to half that of the celling. If the coefficient of restitution is\[{{\left( \frac{1}{2} \right)}^{1/x}}\]. Find the value of x.
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