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A particle is dropped from the top of a tower 60 m high and another is projected upwards from the foot of the tower to meet the first particle at a height of 15.9 m. The velocity of projection of the second particle is
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The reaction at the support D of the continuous beam ABCD, hinged at two points shown in below figure is
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A particle moves along a straight line such that distance x traversed in t seconds is given by x = t2(t + 1), the acceleration of the particle, will be
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For the given values of initial velocity of projection and angle of inclination of the plane, the maximum range for a projectile projected upwards will be obtained, if the angle of projection is
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A shell travelling with a horizontal velocity of 100 m/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan1 x, where x is
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If three rigid rods are hinged together to form a triangle and are given rotary as well as translatory motion, the number of instantaneous centres of the triangle, will be
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μ is coefficient of friction. A wheeled vehicle travelling on a circular level track will slip and overturn simultaneously if the ratio of its wheel distance to the height of its centroid, is
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If the velocity of projection is 4 m/sec and the angle of projection is α°, the maximum height of the projectile from a horizontal plane, is
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A stone was thrown vertically upwards from the ground with a velocity of 50 m/sec. After 5 seconds another stone was thrown vertically upwards from the same place. If both the stones strike the ground at the same time, then the velocity with which the second stone was thrown should be (Assume g = 10 m/sec²)
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For a particle moving with a simple harmonic motion, the frequency is
A. Directly proportional to periodic time
B. Inversely proportional to periodic time
C. Inversely proportional to its angular velocity
D. Directly proportional to its angular velocity
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The time period of a simple pendulum depends on (i) Mass of suspended particle (ii) Length of the pendulum (iii) Acceleration due to gravity The correct answer is
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A stone is thrown vertically upwards with a vertical velocity of 49 m/sec. It returns to the ground in
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A smooth cylinder lying on its convex surface remains
B. In unstable equilibrium
C. In neutral equilibrium
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Periodic time of body moving with simple harmonic motion, is
A. Directly proportional to its angular velocity
B. Directly proportional to the square of its angular velocity
C. Inversely proportional to the square of its angular velocity
D. Inversely proportional to its angular velocity
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Which one of the following laws is not applicable to a simple pendulum?
A. The time period does not depend on its magnitude
B. The time period is proportional to its length l
C. The time period is proportional to l, where l is length
D. The time period is inversely proportional to g, where g is the acceleration due to gravity
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A stone of mass 1 kg is tied to a string of length 1 m and whirled in a horizontal circle at a constant angular speed 5 rad/sec. The tension in the string is,
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Energy may be defined as
B. Capacity of doing work
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The C.G. of a right circular cone lies on its axis of symmetry at a height of
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A body of weight 14 g appears to weight 13 g when weighed by a spring balance in a moving lift. The acceleration of the lift at that moment was
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The centre of gravity of a quadrant of a circle lies along its central radius at a distance of
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A heavy ladder resting on floor and against a vertical wall may not be in equilibrium if
A. Floor is smooth and wall is rough
B. Floor is rough and wall is smooth
C. Both floor and wall are rough
D. Both floor and wall are smooth
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The ratio of the speed of a rolling cylinder to the speed of sliding cylinder is
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From the circular plate of a diameter 6 cm is cut out a circular plate whose diameter is equal to radius of the plate. The C.G. of the remainder shifts from the original position through
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If α and u are angle of projection and initial velocity of a projectile respectively, the total time of flight, is given by
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The necessary condition of equilibrium of a body is:
A. Algebraic sum of horizontal components of all the forces must be zero
B. Algebraic sum of vertical components of all the forces must be zero
C. Algebraic sum of the moments of the forces about a point must be zero
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If the gravitational acceleration at any place is doubled, the weight of a body, will
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The tension in a cable supporting a lift
A. Is more when the lift is moving downwards
B. Is less when the lift is moving upwards
C. Remains constant whether its moves downwards or upwards
D. Is less when the lift is moving downwards
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A disc of mass 4 kg, radius 0.5 m and moment of inertia 3 kgm² rolls on a horizontal surface so that its center moves with speed 5 m/see. Kinetic energy of the disc is
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A particle moves with a velocity of 2 m/sec in a straight line with a negative acceleration of 0.1 m/sec2. Time required to traverse a distance of 1.5 m, is
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The mechanical advantage of an ideal machine is 100. For moving the local through 2 m, the effort moves through