A boy is pushing a ring of mass $$3 \mathrm{~kg}$$ and radius $$0.6 \mathrm{~m}$$ with a stick as shown in figure. The stick applies a force of $$3 \mathrm{~N}$$ on the ring and rolls it without slipping with an acceleration of 0.4 m/s$$^2$$. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is $$\frac{F}{10}$$. The value of $$F$$ is

A load of mass $m$ falls from a height $$h$$ on the scale pan hung from a spring as shown. If the spring constant is $$k$$ and mass of the scale pan is zero and the mass $$m$$ does not bounce relative to the pan, then the amplitude of vibration is

In an experiment to measure the height of a bridge by dropping stone into water underneath. If the error in measurement of time is $$0.2 \mathrm{~s}$$ at the end of $$4 \mathrm{~s}$$, then the error in estimation of height of bridge will be (neglect the water resistance, i.e. thrust)

A conductor lies along the z-axis at $$-1.5 \leq Z \leq 1.5 \mathrm{~m}$$ and carries a fixed current of 10.0 $$\mathrm{A}$$ in $$-a_z$$ direction as shown in figure for a field $$B=3 \times 10^{-4} e^{-0.2 x} a_y \mathrm{~T}$$, the total power required to move the conductor at constant speed to $$x=2.0 \mathrm{~m}, y=0 \mathrm{~m}$$ in $$5 \times 10^{-3} \mathrm{~s}$$ is (Assume parallel motion along the $$x$$-axis)