U Tube SHM

Q. A particle undergoes mutually perpendicular simple harmonic motions given by $x=a\cos \omega t$ and $y=a\sin \omega t$. The trajectory of motion of the particle will be

1. an ellipse
2. a parabola
3. a circle
4. a straight line

Q. A particle undergoes mutually perpendicular simple harmonic motions given by $x=a\cos \omega t$ and $y=a\sin \omega t$. The trajectory of motion of the particle will be

1. an ellipse
2. a parabola
3. a circle
4. a straight line

Q. The figure shows a $U-$ tube of uniform cross-sectional area $A$ having a liquid of mass $M$ and density $\rho$. If the liquid in the column is slightly displaced, then it oscillates with a time period of :
[$g=$ acceleration due to gravity]

1. $T=2\pi \sqrt{\frac{M}{g}}$
2. $T=2\pi \sqrt{\frac{MA}{g\rho }}$
3. $T=2\pi \sqrt{\frac{M}{A\rho g}}$
4. $T=2\pi \sqrt{\frac{M}{2A\rho g}}$

Q. The figure shows a $U-$ tube of uniform cross-sectional area $A$ having a liquid of mass $M$ and density $\rho$. If the liquid in the column is slightly displaced, then it oscillates with a time period of :
[$g=$ acceleration due to gravity]

1. $T=2\pi \sqrt{\frac{M}{g}}$
2. $T=2\pi \sqrt{\frac{MA}{g\rho }}$
3. $T=2\pi \sqrt{\frac{M}{A\rho g}}$
4. $T=2\pi \sqrt{\frac{M}{2A\rho g}}$