A body weighing 8 g when placed in one pan and 18 g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, then the true weight of the body is
13 g
9 g
22 g
12 g
D.
12 g
Consider the diagram in balance
8x = wy
⇒ ...(i)
Also, wx = 18 y
⇒ ....(ii)
Dividing Eq. (i) and Eq. (ii) we get
⇒ 1 =
⇒ w =
w = 12 g
Universal time is based on
rotational effect of the earth about its axis
vibrations of cesium atom
orbital motion of the earth around the sun
oscillation of quartz crystal
A.
rotational effect of the earth about its axis
Time defined in terms of the rotation of the earth is called Universal Time (UT).
A liquid of density 800 kg/m3 is filled in a cylindrical vessel upto a height of 3 m. This cylindrical vessel stands on a horizontal plane. There is a circular hole on the side of the vessel. What should be the minimum diameter of the hole to move the vessel on the
floor, if plug is removed. Take the coefficient of friction between the bottom of the vessel and the plane as 0.5 and total mass of vessel plus vessel as 95 kg.
0.107 m
0.053 m
0.206 m
0.535 m
A.
0.107 m
Given:-
ρ = 800 kg/m3
h = 3 m
μ = 0.5
m = 95 kg
dmin = ?
Let area of hole be a
∴ Reaction force F = ρ av2
= ρa. 2gh [v = ]
and fmax = μN
= μ mg
μ= coefficient of friction
⇒ F ≥ fmax
⇒ 2 ρ agh ≥ μ mg
⇒ a ≥
=
a = 0.009
r2 ≥ 0.009
r ≥
rmin ≥ 0.0535 m
dmin = 2 rmin
= 2 × 0.0535
dmin = 0.107 m
The figure shows a horizontal force F acting on a block of mass M on an inclined plane (angle θ). What is the normal reaction N on the block?
mg sinθ + F cosθ
mg sinθ Fcosθ
mg cosθ F sinθ
mg cosθ + F sinθ
D.
mg cosθ + F sinθ
From the figure, the normal reaction on the block is
N = mg cosθ + F sinθ
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