JEE Advanced 2012 Paper 1 Physics Q5

Physics · Kinematics · Oscillations

Problem

A small block is connected to one end of a massless spring of un-stretched length

4.9\,\mathrm m

. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by

0.2\,\mathrm m

and released from rest at

t=0

. It then executes simple harmonic motion with angular frequency

\omega=\pi/3\,\mathrm{rad/s}

. Simultaneously at

t=0

, a small pebble is projected with speed

v

from point

P

at an angle of

45^\circ

as shown in the figure. Point

P

is at a horizontal distance of

10\,\mathrm m

from

O

. If the pebble hits the block at

t=1\,\mathrm s

, the value of

v

is (take

g=10\,\mathrm{m/s^2}

)