A force $$\mathbf{F}=-k(y \hat{\mathbf{i}}+x \hat{\mathbf{j}})$$ 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 work done by the force on the particle is
With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $$2 / 3$$ of the weight?
Four blocks of same mass connected by strings are pulled by a force $$F$$ on a smooth horizontal surface as shown in figure. The tension $$T_1, T_2$$ and $$T_3$$ will be
What is the maximum height attained by a body projected with a velocity equal to one-third of the escape velocity from the surface of the earth? (Radius of the earth $$=R$$ )