A particle of mass m is initially situated at point P inside a hemispherical surface of radius r as shown in the figure. A horizontal acceleration of magnitude a0 is suddenly produced on the particle in the horizontal direction. If gravitational acceleration is neglected, then time taken by the particle to touch the sphere again is

Question

A particle of mass m is initially situated at point P inside a hemispherical surface of radius r as shown in the figure. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/baef1e82fc0cf89b87cbf7706f2dbe13-.jpeg" /> A horizontal acceleration of magnitude a0 is suddenly produced on the particle in the horizontal direction. If gravitational acceleration is neglected, then time taken by the particle to touch the sphere again is (A)  √(4r sin α/a0)  (B)  √(4r tan α/a0)  (C)  √(4r cos α/a0)  (D) None of these

Tardigrade Admin · Accepted Answer

s=2r cos α ∵ s=(1/2)a0t2 or 2r cos α=(1/2)a0t2 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/9bbe003655feb16b716bbb91f83ca4e5-.jpeg" /> ∴ t=√(4r cos α/a0)

$\frac{4 r s in α}{a _{0}}$

$\frac{4 r t an α}{a _{0}}$

$\frac{4 r cos α}{a _{0}}$

None of these

$s = 2 r cos α$
$∵ s = \frac{1}{2} a_{0} t^{2}$ or $2 r cos α = \frac{1}{2} a_{0} t^{2}$

$∴ t = \frac{4 r cos α}{a _{0}}$

a0​4rsinα​​

a0​4rtanα​​

a0​4rcosα​​

None of these

s=2rcosα ∵s=21​a0​t2 or 2rcosα=21​a0​t2 ∴t=a0​4rcosα​​

$\frac{4 r s in α}{a _{0}}$

$\frac{4 r t an α}{a _{0}}$

$\frac{4 r cos α}{a _{0}}$

$s = 2 r cos α$
$∵ s = \frac{1}{2} a_{0} t^{2}$ or $2 r cos α = \frac{1}{2} a_{0} t^{2}$

$∴ t = \frac{4 r cos α}{a _{0}}$