If torque is takne relative with reference point and this point is displaced, the condition of rotation be valid?

A large , heavy box is sliding without friction down a smooth plane of inclination theta . From a point P on the bottom of the box , a particle is projected inside the box . The initial speed of the particle with respect to the box is u , and the direction of projection makes an angle alpha with the bottom as shown in Figure . (a) Find the distance along the bottom of the box between the point of projection p and the point Q where the particle lands . ( Assume that the particle does not hit any other surface of the box . Neglect air resistance .) (b) If the horizontal displacement of the particle as seen by an observer on the ground is zero , find the speed of the box with respect to the ground at the instant when particle was projected .

Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed omega . The discs are in the same horizontal plane. At time t = 0 , the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is v_(r) . In one time period (T) of rotation of the discs , v_(r) as a function of time is best represented by

In case of an ideal spring, we take the reference point (where potential energy is assumed to be zero) at extension of x_(0) instead of taking at natural length. Then potential energy when spring is extended by x is :

Why it is necessary for reference point in definition of angular momentum?

In a parallelogram OABC, vectors vec a, vec b, vec c are respectively the positions of vectors of vertices A, B, C with reference to O as origin. A point E is taken on the side BC which divide the line 2:1 internally. Also the line segment AE intersect the line bisecting the angle O internally in point P. If CP, when extended meets AB in point F. Then The position vector of point P, is

A cuboidal elevator cabon is shown in the figure. A ball is thrown from point A on the floor of cabon when the elevator is falling under gravity. The plane of motions is ABCD and the angle of projection of the ball with AB, relative to elevator, if the ball collides with point C, is alpha . Then find the value of tan alpha .

A metallic plate having shap of a square is suspended as shown in figure. The plate is made to dip iin water such that level of water is well above that of the plate. The point x is then slowly raised at constant velocity sketch the variation T in string with the displacement S of point x.

In the figure, what will be the sign of the velocity of the point P_1 , which is the projection of the velocity of the reference particle P. P is moving in a circle of radius R in anti-clockwise direction. .

A light ray I is incident on a plane mirror M .The mirror is rotated in the direction as shown in the figure by an arrow at frequency (9)/(pi) "rev"//"sec" ,The light reflected by the mirror is received on the wall W at a distance 10m from the axis of rotation .When the angle of incidence becomes 37^(@) find the speed of the spot (a point) on the wall?

Three points A,B, and C have position vectors -2veca+3vecb+5vecc, veca+2vecb+3vecc and 7veca-vecc with reference to an origin O. Answer the following questions? Which of the following is true?