The position vector of a particle with respect to origin "0" is `vec r`.If the torque acting on the particle is zero,then

The position vector of a particle is r = a sin omega t hati +a cos omega t hatj The velocity of the particle is

The position vector vecr of a particle points along the positive direction of a z axis. If the torque on the particle is (a) zero, (b) in the negative direction of x, and ( c) in the negative direction of y, in what direction is the force causing the torque?

The position vector of a particle is vec( r) = a cos omega t i + a sin omega t j , the velocity of the particle is

The position vector of a particle P with respect to a stationary point O change with time according to the law vec(r) = vec(b) sin omega t + vec(c) cos omega t where vec(b) and vec(c) are constant vectors with b pot c and omega is a positive constant. Find the equation of the path of the particle y = f (x) , assuming x an dy axes to coincide with the direction of the vector vec(b) and vec(c) respectively and to have the origin at the point O

A force (hati-2hatj+3hatk) acts on a particle lying at origin. What is the torque acting on the particle.

The position Vectors of two identical particles with respect to the origin in the three-dimensional coordinator system are r_1and r_2 The position of the centre of mass of the system is given by

Path traced by a moving particle in space is called trajectory of the particle. Shape of trajectiry is decided by the forces acting on the particle. When a coordinate system is associated with a particle motion, the curve equation in which the particle moves [y=f(x)] is called equation of trajectory. It is just giving us the relation among x and y coordinates of the particle i.e. the locus of particle. To find equation of trajectory of a particle, find first x and y coordinates of the particle as a function of time eliminate the time factor. The position vector of car w.r.t. its starting point is given as vec(r)=at hat(i)- bt^(2) hat(j) where a and b are positive constants. The locus of a particle is:-

A force (hati-2hatj+3hatk) acts on a particle of position vector (3hati+2hatj+hatk) . Calculate the hatj^(th) component of the torque acting on the particle.

A force vec((F)) = - K(yhat(i) + x hat(j)) (where K is a positive constant) acts on a particle moving in the X-Y plane. Starting from the origin, the particle is taken along the positive X-axis to the point (a, 0) and then parallel to the Y-axis to the point (a,a). The total done by the force vec(F) . of the particle is

A force vec(F)=4hati-10 hatj acts on a body at a point having position vector -5hati-3hatj relative to origin of co-ordinates on the axis of rotation. The torque acting on the body is