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Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m/sec and 1 m/sec respectively, towards each other along the line of their centers. After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is
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4
If the radius of the earth is 600 km the height of a mountain above sea level at the top of which a beat seconds pendulum at sea level, looses 27 seconds a day, is
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4
In a lifting machine with efficiency 60%, an effort of 200 N is required to raise a load of 6 kN. The velocity ratio of the machine is
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4
Maximum efficiency of a screw jack for the angle of friction θ, is
C. (1 + sin θ)/(1 - sin θ)
D. (1 - sin θ)/(1 + sin θ)
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4
The C.G. of a right circular cone lies on its axis of symmetry at a height of
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4
In SI units, the units of force and energy are respectively
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4
A circular disc rotates at n rpm. The angular velocity of a circular ring of same mass and radius as the disc and to have the same angular momentum is
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4
The motion of a particle is described by the relation x = t2- 10t + 30, where x is in metres and t in seconds. The total distance travelled by the particle from t = 0 to t = 10 seconds would be
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If two forces P and Q (P > Q) act on the same straight line but in opposite direction, their resultant, is
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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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4
If α is the angular acceleration of a compound pendulum whose angular displacement is θ, the frequency of the motion is
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A vehicle weighing w kg is to run on a circular curve of radius r. If the height of its centre of gravity above the road level is h and the distance between the centres of wheels is 2a, the maximum velocity, in order to avoid over turning, will be
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4
A marble ball is rolled on a smooth floor of a room to hit a wall. If the time taken by the ball in returning to the point of projection is twice the time taken in reaching the wall, the coefficient of restitution between the ball and the wall, is
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4
Angular acceleration of a particle may be expressed as
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Instantaneous center is at infinity when the angular velocity is
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From a circular plate of a diameter 6 cm is cut out a circle whose diameter is equal to the radius of the plate. The C.G. of the remainder from the centre of circular plate is at a distance of
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4
A glass ball is shot to hit a wall from a point on a smooth floor. If the ball returns back to the point of projection in twice the time taken in reaching the wall, the coefficient of restitution between the glass ball and the wall is
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4
A simple pendulum of length 1 has an energy E when its amplitude is A. If its amplitude is increased to 2 A, the energy becomes
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4
M.I. of a thin ring (external diameter D, internal diameter d) about an axis perpendicular to the plane of the ring, is
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4
A point subjected to a number of forces will be in equilibrium, if
A. Sum of resolved parts in any two directions at right angles, are both zero
B. Algebraic sum of the forces is zero
C. Two resolved parts in any two directions at right angles are equal
D. Algebraic sum of the moments of the forces about the point is zero
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4
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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4
One Joule is equivalent to
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The centre of gravity of the trapezium as shown in below figure from the side is at a distance of
A. (h/3) × [(b + 2a)/(b + a)]
B. (h/3) × [(2b + a)/(b + a)]
C. (h/2) × [(b + 2a)/(b + a)]
D. (h/2) × [(2b + a)/(b + a)]
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If two forces each equal to T in magnitude act at right angles, their effect may be neutralised by a third force acting along their bisector in opposite direction whose magnitude will be
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Select the correct statement
A. The body centrode rolls on the space centrode
B. The space centrode rolls on the body centrode
C. Both body and space centrodes may role on each other
D. The body centrode never touches space centrode
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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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When a body in equilibrium undergoes an infinitely small displacement, work imagined to be done, is known as
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A rod 5 m in length is moving in a vertical plane. When it is inclined at 60° to horizontal, its lower end is moving horizontally at 3 m/sec and upper end is moving in vertical direction. The velocity of its upper end, is
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The resultant of two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then,
D. None of the above is correct
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Pick up the incorrect statement from the following. In a simple harmonic motion
A. Velocity is maximum at its mean position
B. Velocity is minimum at the end of the stroke
C. Acceleration is minimum at the end of the stroke
D. Acceleration is zero at the mean position