A particle of mass m is initially situated at the point P inside a hemispherical surface of radius r as shown in figure. A horizontal acceleration of 

magnitude a_o is suddenly produced on the particle in the horizontal direction. If gravitational acceleration is neglected, then time taken by particle to touch the sphere again is
where a is the angle which OP makes with radius OC.

• A

  $\sqrt{\left(\frac{4\mathrm{rsin}\mathrm{\alpha }}{{\mathrm{a}}_0}\right)}$

• B

  $\sqrt{\left(\frac{4\mathrm{rtan}\mathrm{\alpha }}{{\mathrm{a}}_0}\right)}$

• C

  $\sqrt{\left(\frac{4\mathrm{rcos}\mathrm{\alpha }}{{\mathrm{a}}_0}\right)}$

• D

  $\sqrt{\left(\frac{4\mathrm{rcot}\mathrm{\alpha }}{{\mathrm{a}}_0}\right)}$