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Toppr Admin · Accepted Answer

F-x2212-amr-x21D2-Fx-i-Fy-j-x2212-am-x-i-y-j-x21D2-md2xdt2-i-md2ydt2-j-x2212-am-x-i-y-j-

A particle of mass m moves according to the equation F=−amr where a is a positive constant,r is radius vector. r=r0^i and v=v0^j at t=0. Describe the trajectory.(xr0)2+a(yv0)2=1(xr0)2+a(yv0)2=0(xr0)2+(yv0)2=1αnoneofthese

F=−amr⇒Fx^i+Fy^j=−am(x^i+y^j)⇒md2xdt2^i+md2ydt2^j=−am(x^i+y^j)

$F = - a m r \Rightarrow F_{x}^i + F_{y}^j = - a m (x^i + y^j) \Rightarrow m \frac{d^{2} x}{d t^{2}}^i + m \frac{d^{2} y}{d t^{2}}^j = - a m (x^i + y^j)$