IIT-JEE Exam

A small block is connected to one end of a massless spring of un-stretched length 4.9 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
m and released from rest at t = 0. It then executes simple harmonicmotion with angular frequency rad/ s
pie/3.
Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of 45ยบ as shown in the
figure. Point P is at a horizontal distance of 10 cm from O. If the pebble hits the block at t = 1s, the value of v is

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IIT-JEE Other Question
A mixture of 2 moles of helium gas (atomic mass = 4 amu), and 1 mole of argon gas (atomic mass = 40 amu)
is kept at 300 K in a container. The ratio of the rms speeds is Three very large plates of same area are kept parallel and close to each other. They are considered as ideal
black surfaces and have very high thermal conductivity. The first and third plates aremaintained at temperatures
2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is