The equation of a circle with origin as a center and passing through equilateral triangle whose median is of length 3a is
A chain of linear density 3 kg /m and length 8 m is lying on the table with 4 m of chain hanging from the edge. The work done in lifting the chain on the table will be ?
An automobile of mass m accelerates from rest. If the engine supplies a constant power P, the velocity at time t is given by
A force F =(7–2x+3x*x )N is applied on a 2kg mass which displaces it from x = 0 to x = 5 m. Work done in joule is ?
The work done in pulling a body of mass 5 kg along an inclined plane (angle 60) with coefficient of friction 0.2 through 2 m,will be?
A body is acted upon by a force F=-i+2j+3k.The work done by the force in displacing it from (0,0,0) to (0,0,4m) will be?
If the chord y = mx + 1 of the circle x2 + y2 = 1 subtends an angle of measure 45° at the major segment of the circle then value of m is
An object of mass 5 kg falls from rest through a vertical distance of 20 m and reaches a velocity of 10 m/s. How much work is done by the push of the air on the object ? (g = 10 m/s2).
The work done in lifting water from a well of depth 6 m using a bucket of mass 0.5 kg and volume 2 litre, will be
A particle moves in the X-Y plane under the influence of a force such that its linear momentum is p(t ) = A[i cos(kt ) - j sin(kt )] , where A and k are constants. The angle between the force and the momentum is?
A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is u . The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 u, then N is
A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is . The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 , then N is
When 30.0 g of a nonvolatile solute having the empirical formula CH20 of water ,the solution freezes it-1.16°C. What is the molecular formula of solute
The vector lies in the plane of the vectors and and bisects the angle between and . Then which one of the following gives possible values of and ?
The values of a, for which the points A, B, C with position vectors and respectively are the vertices of a right angled triangle at c are
Let be such that If the projection along is equal to that of along and , are perpendicular to each other then equals
A particle is acted upon by constant forces and which displace it from a point to the point The work done in standard units by the forces is given by
Let and be three non-zero vectors such that no two of these are collinear. If the vector is collinear with and is collinear with ( being some nonzero scalar) then equals
A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point, Then tensions in the strings are
A particle just clears a wall of height b at a distance a and strikes the ground at a distance c from the point of projection. What will be the angle of projection?
A body falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4 s prior to passing through P. If g = 10 m/s 2, then the height above the point P from where the body began to fall is
A particle has two velocities of equal magnitude inclined to each other at an angle q. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then q is
A particle is projected from a point O with velocity u at an angle of 60º with the horizontal. When it is moving in a direction at right angles to its direction at O, its velocity then is given b
A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s 2 and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/ s. Then when the lizard will catch the insect?
Two points A and B move from rest along a straight line with constant acceleration f and f' respectively. If A takes msec. more than B and describes n units more than B in acquiring the same speed then
A velocity 1/4 m/s is resolved into two components along OA and OB making angles 30º and 45º respectively with the given velocity. Then the component along OB is
A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5 km/h. If AB = 12 km andBC= 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively
Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity and the other from rest with uniform acceleration . Let be the angle between their directions of motion. The relative velocity of the second particle with respect to the first is least after a time