A uniform square plate ABCD has mass M side length `a`. It is sliding on a horizontal smooth surface with a velocity of`vec(v) = v_(0) (4 hat(i) + 2 hat(j))`. There is no rotation. Vertex A of the plate is suddenly fixed by a nail. Calculate the velocity of centre of the plate immediately after this

A surface has the area vector vec(A) = (2 hat(i) + 3 hat(j)) m^(2) . The flux of an electric field through it if the field is vec(E) = 4 hat(i) (V)/(m) :

An electron of charge -e , mass m, enters a uniform magnetic field vec(B)= B hat(i) with an initial velocity vec(v) = v_(x) hat(i) + v_(y) hat(j) . What is the velocity of the electron after a time interval of t seconds?

A particle of mass m moves in the xy-plane with velocity of vec v = v_x hat i+ v_y hat j . When its position vector is vec r = x vec i + y vec j , the angular momentum of the particle about the origin is.

A smooth sphere is moving on a horizontal surface with velocity vector 3hat(i) + hat(j) immediately before it hits a vertical wall. The wall is parallel to the vector hat(j) and the coefficient of restitution between the wall and sphere is (1)/(3) . The velocity vector of the sphere after it hits the wall is :-

A motor boat is going in a river with a velocity vec(V) = (4 hat i-2 hat j + hat k) ms^(-1) . If the resisting force due to stream is vec (F)=(5 hat i-10 hat j+6 hat k)N , then the power of the motor boat is

A 150 g mass has a velocity vec(v)=(2hat(i)+6hat(j))m//s at a certain instant. What is its kinetic energy?