Physics Solved Problems on Force, Gravitational Force, Angular Speed, Specific Heat, Telescope Lens and Spring Constant

Ques. 1
(a)
⃗
F=3 i+ 4 j
m=2 kg
⃗
a=?
⃗
F=m ⃗ a
Where F is force on a body
m is mass of body
And a is acceleration
So,
3 i+ 4 j=2 ⃗ a
1
2 (3 i+4 j )= ⃗ a
1.5 i+ 2 j= ⃗ a
Magnitude is
a= √ ( 1.5 )2+ ( 2 )2
a=2.5 m/ s2
According to newton’s 2nd law of motion.
The direction is same as direction of force.
So,
tanθ= y
x
tanθ= 2
1.5
tanθ=1.33
θ=tan−1 1.33
θ=53.130 ¿ x−axis
Ques.2
(b)
The planet revolve around the sun which have relation between time period (T) and distance
between sun and planet radius (r) (for circular orbits) is

T 2=r3
Let us consider mass of orbit is m.
And mass of sun is M.
We know that M >>>> m
Radial force is equal to gravitational force
GMm
r2 =m ω2 r
ω2=GM
r3 ..................(1)
T = 2 π
ω
ω= 2 π
T .................(2)
From equation (1) and (2)
(2 π )2
T2 = GM
r3
T 2= 4 π2 r3
GM
So we have that
T 2=r3
Distance of Uranus from earth is 20AU
Distance of Pluto from earth is 40AU
So,
TUranus
2
T Pluto
2 = 203
403
TUranus
2
T Pluto
2 = 8
64 = 1
8
TUranus
2
T Pluto
2 = 1
2 √ 2
Ques. 3
(a)

Mass = 5kg
Diameter = 0.4m
r = d/2
r = 0.2m
n1=2rev /sec
The angular speed increases 8 revolutions per second in 2sec.
n2 =8 rev /sec
ω=2 πn
ω1=2 π ×2
ω1=4 π
ω2=2 π × 8
ω2=16 π
Angular acceleration (∝)
∝= ω2−ω1
t
∝=(16 π −4 π )
2
∝= 2 π (8−2)
2
∝=6 π rad /s2
Moment of inertia of wheel is
I =M r2
I =5 ×0.22
I =0.2 N / m2
Torque ( τ )=I ×∝
τ =0.2 ×6 π
τ =3.77 Nm
Ques. 4