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A particle P ...

Question

A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at $t = 0$ . At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at $t = 0$ along the horizonal string AB, with the speed v. Friction between the bead and the string may be neglected. Let $t_{P}$ and $t_{Q}$ be the respective times taken by P and Q to reach the point B. Then?

t_{P} < t_{Q}

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t_{P} = t_{Q}

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t_{P} > t_{Q}

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\frac{t_{P}}{t_{Q}} = \frac{l e n g t h o f a r c A C B}{l e n g t h o f c h o r d A B}

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Solution

The correct option is A $t_{P} < t_{Q}$
the mass of the particle P and the bead Q is the same and it is also given that they have the same velocity. the object is a hemispherical bowl.L et D1 be distance travelled by the particle P with mass m and velocity v.D1 = stand D2 be the distance travelled by the bead Q with mass m and velocity since D2 is actually the displacement of Particle P and distance of bead B<= distance displacement of P < distance travelled by P==> distance travelled by bead Q < distance travelled by P velocity is the same.

the time taken to travel a smaller distance is less than time is taken to travel a larger distance. therefore time taken by Particle P > time taken by bead Q
option {B} t(P) > t(Q)

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Q. A particle

P

is sliding down a frictionless hemispherical bowl. It passes the point

A

t = 0

. At this instant of time, the horizontal component of its velocity is

v

A

bead

Q

of the same mass as

P

is ejected from

A

t = 0

along the horizontal string

AB

(see figure) with the speed

v

. Friction between the bead and the string may be neglected. Let

t_{P}

and

t_{Q}

be the respective time taken by

P

and

Q

to reach the point

B

. Then

A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t = 0 along the horizontal string AB, with a speed v. Friction between the bead and the string may be neglected. Let tp and tq be the respective times taken by P and Q to reach the point B. Then

Time taken by p is

a) less than Q

b) greater than Q

c)equal to Q

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