A block of mass 2 kg lies on a smooth horizontal table and is connected to another freely hanging block of mass 1 kg by a light inextensible string passing over a smooth fixed pulley as shown in figure. Initially system is at rest and 2 kg mass is at a distance of 2 m from the pulley. The time taken by 2 kg block to reach the pulley is 2 kg 2 m
Answers
Answer:
The correct option is A
A
c
c
e
r
l
e
r
a
t
i
o
n
=
m
2
m
1
+
m
2
×
g
=
1
2
+
1
×
9.8
=
3.27
m
/
s
2
and
T
=
m
1
a
=
2
×
3.27
=
6.54
N
Given:
A block of mass 2 kg on a smooth horizontal table connected to another freely hanging block of mass 1 kg by a light inextensible string passing over a smooth fixed pulley
To Find:
The time taken by 2 kg block to reach the pulley if initially, the system is at rest.
Solution:
The time taken by 2 kg block to reach the pulley is 1.09s.
Considering the two masses as a part of a single system, and applying Newton's second law of motion the equation obtained is:
1g = (2 + 1) a
Here g is the acceleration due to gravity and a is the acceleration of the system.
Substituting g = 10 m/s² we get:
a = 10/3 m/s²
Since the system has a constant acceleration, we can apply the 2nd equation of motion, s = ut + 0.5 at²
Taking u = 0 m/s
2 = 0 + 0.5 X 10/3 t²
or 2 = 5/3 t²
or t² = 6/5
or t = √1.2