IIT-JEE 2011 - Career Point

2
L A = m A ω r A
2
L B = m B ωr B
Ratio (K) =
r
r
m
=
m
A
L A + L
L
11
=
2.2
B
A B
=
B
5
B
=
Ratio (K) = 5
1 × 5 2 + 1 = 6
2
L A m + 1 =
ArA
2
LB
mBrB
+ 1
Ans. [8]
Sol. The amount of heat required to raise the temp
from –5°C to 0°C.
Q 1 = m × 2100 × 10 –3 × 5 = 10.5 m Joule
The amount of heat required to melt 1 gm
ice = 10 –3 × 3.36 × 10 5 = 336 J
420 = 336 + 10.5 m
10.5 = 84
m = 8 gm.00
83. Gravitational acceleration on the surface of a
planet is 11
6 g, where g is the gravitational
acceleration on the surface of the earth. The
2
average mass density of the planet is times 3
that of the earth. If the escape speed on the
surface of the earth is taken to be 11 km/s, the
escape speed on the surface of the planet in km/s
will be ?
Ans. [3]
Sol.
υ p 2g pR
p =
υc
2geR
e
(1)
⇒
M
4
πR
3
p
3
p
= 3
2
=
g p R p × …
g
e
Me
4
πR
3
3
e
R
e
M P 2 R
⇒ =
M 3 R
GM p 6 GM M
2 =
e p 6 R
R p 11
2 ⇒ =
R M
e
c 11 R
from (2) and (3)
3
p
2 R 6
3 =
3 R e 11 R
from (1) and (4)
2
p
2
e
R R p 3 ⇒ =
R e 226
υ p 6 3 18 3
= × = =
υe
11 226
242 11
v p = 3 km /sec.
e
2
p
2
e
3
p
3
e
… (4)
… (2)
…(3)
84. A piece of ice (heat capacity = 2100 Jkg –1 ºC –1 and
latent heat = 3.36 × 10 8 J kg –1 ) of mass m grams
is at –5ºC at atmospheric pressure. It is given 420
J of heat so that the ice starts melting. Finally
when the ice-water mixture is in equilibrium, it is
found that 1 gm of ice has melted. Assuming
there is no other heat exchange in the process, the
value of m is ?
ATTITUDE
• Great effort springs naturally from a great
attitude.
• Like success, failure is many things to many
people. With Positive Mental Attitude, failure
is a learning experience, a rung on the ladder,
a plateau at which to get your thoughts in
order and prepare to try again.
• Your attitude, not your aptitude, will
determine your altitude.
• Develop an attitude of gratitude, and give
thanks for everything that happens to you,
knowing that every step forward is a step
toward achieving something bigger and better
than your current situation.
• You can adopt the attitude there is nothing
you can do, or you can see the challenge as
your call to action.
• "An optimist is a person who sees a green
light everywhere, while the pessimist sees
only the red stoplight... The truly wise person
is colorblind."
• Positive thinking will let you do everything
better than negative thinking will.
• You cannot control what happens to you, but
you can control your attitude toward what
happens to you, and in that, you will be
mastering change rather than allowing it to
master you.
• You can do it if you believe you can!
XtraEdge for IIT-JEE 84
MAY 2010