F=a(ডট(y)-ডট(x) হিসাবে বেগের সাথে পরিবর্তিত বলের কারণে ভর m মুভসিন প্যান xy এর একটি কণা...

A particle of mass m moves in pane xy due to the force varying with velocity as F=a(dot(y)-dot(x)j) , where a is a positve constant, i and j are the unit vectors of the x and y axes. At the initial moment t=0 the particle was located at the point x=y=0 and possessed a velocity v_(0) directed along the unit vector j . Find the law of motino x(t), y(t) of the particle, and also the equation of its trajectory.

A force acting on a certain particle depends of the particles position in the xy-plane. This force F is given by the expression vec(F) = (xy hat(i) + xy hat(j)) (1 N//m^(2)) where x and y are expressed in metre. If vec(F) is a conservation force ?

A particle of mass m = 2kg executes SHM in xy - plane between point A and B under action of force vecF = F_(x)hati+F_(y)hatj . Minimum time taken by particle to move from A to B is 1 sec. At t = 0 the particle is at x = 2 and y = 2 . Then F_(x) as function of time t is

A particle of mass 2kg moves under a force given by vec(F)=-(8N//m)(xhat(i)+yhat(j)) where hat(i) and hat(j) are unit vectors in the x and y directions. The particle is projected from the origin in xy plane with an initial velocity vec(v)=(3m//s)hat(i)+(4m//s)hat(j) . Select correct statement(s).

A particle of mass 2kg moves under a force given by vec(F)=-(8N//m)(xhat(i)+yhat(j)) where hat(i) and hat(j) are unit vectors in the x and y directions. The particle is projected from a point on x axis at x=a in xy plane with an initial velocity vec(v)=v_(0)hat(j) . Select correct statement (s). The particle will move in

If f(2x+(y)/(8),2x-(y)/(8))=xy, then f(m,n)+f(n,m)=0 only when m=n only when m!=n only when m=-n( d) f or allmandn

It is pouring down rain and the amount of rain hitting point (x,y) is given by f (x,y) =|x^(3)+2x ^(2)y- 5xy ^(2)-6y ^(3)|. If Mr. 'A' starts at (0,0), find number of possible value (s) for 'm' such that y= mx is a line along which Mr.' A could walk without any rain falling on him.

if x= 2cos theta ,y= 2sin theta and the range of f(x,y)=x^(2)-xy+y^(2) is [L,M] then the value of the product L.M is equal to