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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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The displacement of a particle which moves along a straight line is given by S = 4t3 + 3t2- 10 where S is in meters and t is in seconds. The time taken by the particle to acquire a velocity of 18 m/sec from rest, is
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4
A particle is executing simple harmonic motion in a line 1.0 m long. If the time of one complete vibration is 1 sec, then the maximum velocity of the particle is
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If a spherical body is symmetrical about its perpendicular axes, the moment of inertia of the body about an axis passing through its centre of gravity as given by Routh's rule is obtained by dividing the product of the mass and the sum of the squares of two semi-axes by n. Where, n is
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4
The forces which meet at one point and have their lines of action in different planes are called
A. Coplanar non-concurrent forces
B. Non-coplanar concurrent forces
C. Non-coplanar non-current forces
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The total kinetic energy of a hoop of mass 2 kg and radius 4 m sliding with linear velocity 8 m/sec and angular velocity 5 radian/sec is
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A particle of mass 2 kg executes simple harmonic motion of frequency 6/71 Hz and amplitude 0.25 m. Its maximum kinetic energy is
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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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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 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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Power can be expressed as
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For the system of the loads shown in below figure, the time required for the 6.6 kg load to fall on the edge, is
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The instantaneous centre of a member lies at the point of intersection of two lines drawn at the ends of the member such that the lines are inclined to the direction of motion of the ends at
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The intrinsic equation of catenary is
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The numbers of funicular polygons which can be drawn to pass through two specified points in the space diagram are
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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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If a ball which is dropped from a height of 2.25 m on a smooth floor attains the height of bounce equal to 1.00 m, the coefficient of the restitution between the ball and floor, is
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The following statement is one of the laws of Dynamic friction
A. The force of friction always acts in a direction opposite to that in which a body is moving
B. The magnitude of the kinetic friction bears a constant ratio to the normal reaction between two surfaces. The ratio being slightly less than that in the case of limiting friction
C. For moderate speeds the force of friction remains constant but decreases slightly with the increase of speed
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The unit of Moment of Inertia of a body, is
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The force which produces an acceleration of 1 m/sec2 in a mass of one kg, is called
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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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The velocity ratio of the differential wheel and axle is
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If α and u are the angle of projection and initial velocity of a projectile respectively, the horizontal range of the projectile, is
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A 2 m long ladder rests against a wall and makes an angle of 30° with the horizontal floor. Where will be the instantaneous center of rotation when the ladder starts slipping? (i) 1.0 in from the wall (ii) 1.732 m from the wall (iii) 1.0 m above the floor (iv) 1.732 m above the floor The correct answer is
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The equation of motion of a particle starting from rest along a straight line is x = t3 - 3l2 + 5. The ratio of the velocities after 5 sec and 3 sec will be
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For lifting a load of 50 kg through a distance of 2.5 cm, an effort of 12.5 kg is moved through a distance of 40 cm. The efficiency of the lifting machine, is
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One end of a light string 4 m in length is fixed to a point on a smooth wall and the other end fastened to a point on the surface of a smooth sphere of diameter 2.25 m and of weight 100 kg. The tension in the string is
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When a body moves round a fixed axis, it has
D. A rotary motion and translatory motion
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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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Two particles have been projected at angles 64° and 45° to the horizontal. If the velocity of projection of first is 10 m/sec, the velocity of projection of the other for equal horizontal ranges is