The resultant of these forces $\overrightarrow{OP}, \overrightarrow{OQ}, \overrightarrow{OR}, \overrightarrow{OS}$ and $\overrightarrow{OT}$ is approximately $\_\_\_\_$ N. [Take $\sqrt{3} = 1.7, \sqrt{2} = 1.4$ Given $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ unit vectors along $x, y$ axis] (1) $-1.5\hat{\mathrm{i}} - 15.5\hat{\mathrm{j}}$ (2) $9.25\hat{i} + 5\hat{j}$ (3) $3\hat{i} + 15\hat{j}$ (4) $2.5\hat{\mathrm{i}} - 14.5\hat{\mathrm{j}}$
A huge circular arc of length 4.4 ly subtends an angle 4 s at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second? Given: $1\mathrm{ly} = 9.46 \times 10^{15}\mathrm{~m}$ $1\mathrm{AU} = 1.5 \times 10^{11}\mathrm{~m}$ (1) $3.5 \times 10^{6}\mathrm{~s}$ (2) $4.5 \times 10^{10}\mathrm{~s}$ (3) $4.1 \times 10^{8}\mathrm{~s}$ (4) $7.2 \times 10^{8}$
Two persons $A$ and $B$ perform same amount of work in moving a body through a certain distance $d$ with application of forces acting at angles $45^{\circ}$ and $60^{\circ}$ with the direction of displacement respectively. The ratio of force applied by person $A$ to the force applied by person $B$ is $\frac{1}{\sqrt{x}}$. The value of $x$ is $\_\_\_\_$.