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TS EAMCET 10-Sep-2020 Shift 2 Solved Paper
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© examsnet.com
Question : 92
Total: 160
An object of mass 2 kg is hanging from a rope that is wrapped around a pulley of radius 25 cm. The mass of pulley is 2 kg. Find the acceleration of the object.
(Assume pulley to be a solid disk; g = 10 m/
s
2
)
2
3
m
/
s
2
4
3
m
/
s
2
10
3
m
/
s
2
20
3
m
/
s
2
Validate
Solution:
Let block falls through a height
h
, then loss of PE of block appears in form of KE of block and KE of rotation of pulley.
⇒
m
g
h
=
‌
1
2
m
v
2
+
‌
1
2
‌
M
R
2
2
â‹…
ω
2
Here,
m
=
M
=
2
k
g
,
So,
‌
‌
g
h
=
‌
v
2
2
+
‌
R
2
4
ω
2
As
v
=
R
ω
,
g
h
=
‌
3
4
R
2
ω
2
Differentiating with respect to time,
g
â‹…
‌
d
h
d
t
‌
‌
=
‌
3
4
R
2
â‹…
2
ω
â‹…
‌
d
ω
d
t
g
v
‌
‌
=
‌
3
4
R
2
×
2
×
‌
v
R
â‹…
α
⇒
‌
‌
g
‌
‌
=
‌
6
4
R
α
⇒
‌
4
g
6
=
R
α
⇒
‌
‌
R
α
=
‌
2
g
3
‌
But
‌
R
α
=
a
t
‌
‌
=
‌
tangential acceleration of pulley
‌
‌
‌
=
‌
acceleration of block
‌
So,
a
t
=
R
α
=
‌
2
3
g
=
‌
20
3
m
∕
s
2
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