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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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4
Two circular discs of same weight and thickness are made from metals having different densities. Which disc will have the larger rotational inertia about its central axis?
A. Disc with larger density
B. Disc with smaller density
C. Both discs will have same rotational inertia
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4
The Centre of gravity of a 10 × 15 × 5 cm T-section from its bottom, is
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4
If the tension in a cable supporting a lift moving upwards is twice the tension when the lift is moving downwards, the acceleration of the lift, is
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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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The locus of the instantaneous centre of a moving rigid body, is
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Free body diagram is an
A. Isolated joint with only body forces acting on it
B. Isolated joint with internal forces acting on it
C. Isolated joint with all the forces, internal as well as external, acting on it
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The height at which the end of a rope of length l should be tied so that a man pulling at the other end may have the greatest tendency to overturn the pillar, is
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The gravitational force makes a satellite go round the earth in a circular orbit, if it is projected with an initial velocity of
A. 8.04 km/sec at a height of 285 km
B. 11.11 km/sec at a height of 37,400 km
C. 11.26 km/sec, the satellite escapes the pull of the earth
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The units of inertia of mass are
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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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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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Varingons theorem of moments states
A. Arithmetical sum of the moments of two forces about any point, is equal to the moments of their resultant about that point
B. Algebraic sum of the moments of two forces about any point, is equal to the moment of their resultant about that point
C. Arithmetical sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
D. Algebraic sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
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The resultant of two forces acting at right angles is √34 kg and acting at 60° is 70 kg. The forces are
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A car goes round a curve of radius 100 m at 25 m/sec. The angle to the horizontal at which the road must be banked to prevent sideways friction on the car wheels is tan1 x, where x is (Assume g = 10 m/sec²)
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At the instantaneous center, the velocity of the moving lamina at any instant is
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The unit of Moment of Inertia of a body, is
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Equation of motion of a point in a straight line, is
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If the angle of projection is double the angle of inclination (α) of the plane on which particle is projected, the ratio of times of flight up the inclined plane and down the inclined plane, will be
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If the resultant of two forces P and Q acting at an angle θ makes an angle α with P, then tan α equals
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A particle is dropped from a height of 3 m on a horizontal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the ball will rebound after striking the floor is
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If the given forces P₁, P₂, P₃ and P₄ are such that the force polygon does not close, then the system will
B. Always reduce to a resultant force
C. Always reduce to a couple
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To attain the synchronous orbit, the launch of a satellite, is done from a place
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The mechanical advantage of an ideal machine is 100. For moving the local through 2 m, the effort moves through
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Ball A of mass 250 g moving on a smooth horizontal table with a velocity of 10 m/s hits an identical stationary ball B on the table. If the impact is perfectly elastic, the velocity of the ball B just after impact would be
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A square hole is made in a circular lamina, the diagonal of the square is equal to the radius of the circle as shown in below figure the shift in the centre of gravity is
A. r (π - 0.75)/(π - 0.5)
B. r (π - 0.25)/(π - 0.75)
C. r (π - 0.5)/(π - 0.75)
D. r (π - 0.5)/(π - 0.25)
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The vertical reaction at the support A of the structure shown in below figure, is
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To double the period of oscillation of a simple pendulum
A. The mass of its bob should be doubled
B. The mass of its bob should be quadrupled
C. Its length should be quadrupled
D. Its length should be doubled
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4
On a ladder resting on a rough ground and leaning against a smooth vertical wall, the force of friction acts
A. Downwards at its upper end
B. Upwards at its upper end
C. Perpendicular to the wall at its upper end
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A hoop of radius 3 m weighs 100 kg. It rolls along a horizontal floor so that at its centre of mass has a speed of 200 mm/sec. The work required to stop the hoop is