- In two systems of relations among velocity,
acceleration, and force are, respectively, vv 2
2
= 1
α
β
,
a 2 = DEa 1 , and F
F
2
=^1
αβ
. If D and E are constants,
then correct relation among mass, length, and time
in two systems is
(a) TT 21 = α 2
β
(b) M
M
2
1
=αβ 22
(c) LL 21 = α 2
β
(d) Both (a) and (b)
- Shots are red simultaneously
from the top and bottom of a
vertical cli with the elevation
D = 30°, E = 60°, respectively
gure. e shots strike an
object simultaneously at the
same point. If a= 30 3m is
the horizontal distance of the object form the cli,
then the height h of the cli is
(a) 30 m (b) 45 m (c) 60 m (d) 90 m - In the gure shown a plank of length l = 64 m, mass
m 2 = 5 kg rests on a smooth surface. Upper surface
of block is rough with coecient of kinetic friction
Pk = 0.5 and Ps = 0.6. A force F of magnitude 30 N is
applied on block m 1. What is displacement of plank
till the small block falls over from plank?
m 2
F m 1 Rough
Smooth
L
(a) 0.6 m (b) 10 m (c) 16 m (d) 2.5 m
- A lead bullet just melts when stopped by an obstacle.
Assuming that 25 percent of the heat is absorbed by
the obstacle, nd the velocity of the bullet. Its initial
temperature is 27°C.
(Melting point of lead = 327°C, specic heat of
lead = 0.03 cal g–1 °C–1, latent heat of fusion of lead
= 6 cal g–1 °C–1, J = 4.2 joule calorie–1).
h
E
D
a= 30 3m
(a) 300 m s–1 (b) 409.8 m s–1
(c) 1100 m s–1 (d) 25 m s–1
- A carpet of mass M, made of inextensible, material
is rolled along its length in the form of a cylinder
of radius R and is kept on a rough oor. e carpet
starts unrolling without sliding on the oor when
a negligibly small push is given to it. Calculate the
horizontal velocity of the axis of the cylindrical part
of the carpet when its radius reduces to R/2.
(a)
14
3
Rg
(b) gR
(c) 3 gR (d) 5 gR
- A body is projected vertically upwards from the
bottom of a crater of moon of depth R/100 where
R is the radius of moon with a velocity equal to the
escape velocity on the surface of moon. Calculate
maximum height attained by the body from the
surface of the moon.
(a) 150 R (b) 99 R (c) 50 R (d) 199 R - A drop of water of mass 0.2 g is placed between two
glass plates. e distance between them is 0.01 cm.
Find the force of attraction between the plates if
surface tension of water = 0.07 N m–1.
(a) 2.8 N (b) 3.5 N (c) 0.7 N (d) 1.25 N - A column of mercury of length 10 cm is contained
in the middle of a horizontal tube of length 1 m
which is closed at both the ends. e two equal
lengths contain air at standard atmospheric pressure
of 0.76 m of mercury. e tube is now turned to
vertical position. By what distance will the column
of mercury be displaced?
(a) 3.14 cm (b) 1.28 cm
(c) 2.95 cm (d) 4.83 cm - A thermostated chamber at a height h above earth's
surface maintained at 30°C has a clock tted with
uncompensated pendulum. e maker of the clock
for chamber mistakenly designed it to maintain
correct time at 20°C. It is found that when the
chamber is brought to earth's surface the clock in it
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