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A bar of mass M and length L is hanging from point S as shown in figure. The Young's modulus of elasticity of the wire is Y and the area of cross-section of the wire is A. Find total elongation in bar.
                            
1.  $\frac{\mathrm{MgL}}{\mathrm{AY}}$
2.  $\frac{\mathrm{MgL}}{2\mathrm{AY}}$
3.  $\frac{2\mathrm{MgL}}{\mathrm{AY}}$
4.  $\frac{3\mathrm{MgL}}{2\mathrm{AY}}$

An automobile of mass m accelerates, starting from rest, while the engine supplies constant power P, its position and velocity changes with respect to time as-
1.  ${\left(\frac{\mathrm{Pt}}{9\mathrm{m}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} {\mathrm{t}}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}, {\left(\frac{2\mathrm{Pt}}{\mathrm{m}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
2.  ${\left(\frac{2\mathrm{Pt}}{9\mathrm{m}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} {\mathrm{t}}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}, {\left(\frac{\mathrm{Pt}}{\mathrm{m}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
3.  ${\left(\frac{8\mathrm{P}}{9\mathrm{m}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} {\mathrm{t}}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}, {\left(\frac{2\mathrm{Pt}}{\mathrm{m}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
4.  ${\left(\frac{8\mathrm{P}}{9\mathrm{m}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} {\mathrm{t}}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}, {\left(\frac{\mathrm{Pt}}{\mathrm{m}}\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

The 9 kg block is moving to the right with a velocity of 0.6 m/s on a horizontal surface when a force F, whose time variation is shown in the graph, is applied to it at time t=0. Calculate the velocity v of the block when t=0.4s. The coefficient of kinetic friction is ${\mathrm{\mu }}_{\mathrm{k}}=0.3.$
                    
1.  0.6 m/s
2.  1.2 m/s
3.  1.8 m/s
4.  2.4 m/s

A point moves in a straight line under the retardation ${\mathrm{av}}^2$. If the initial velocity is u, the distance covered in 't' second is-
1.  aut
2.  $\frac{1}{\mathrm{a}}\ln \left(\mathrm{aut}\right)$
3.  $\frac{1}{\mathrm{a}}\ln \left(1+\mathrm{aut}\right)$
4.  $\mathrm{a} \ln \left(\mathrm{aut}\right)$