1
Question
Figure shows a block of mass m attached to a spring of force constant k and connected to ground by two string. In relaxed state natural length of the spring is l. In the situation shown in figure, find the tension in the strings (1) and (2).
Figure shows a block of mass m attached to a spring of force constant k and connected to ground by two string. In relaxed state natural length of the spring is l. In the situation shown in figure, find the tension in the strings (1) and (2).
Open in App
Solution
The correct option is C T1=√34[kl−2mg],T2=14[kl−2mg]
As the natural length of spring is l, and in the situation shown in figure its length is 3l2. Thus the spring is stretched by a distance l2 hence it exerts a restoring force on block k(l2) upward as shown in figure, which shows also the tensions acting on the block along the directions of the strings. As the block is in equilibrium, we can balance all the forces acting on it along horizontal and vertical directions.
Along horizontal direction
T1 sin 30∘ =T2 sin 60∘
or T1=√3T2.......(1)
Along vertical direction
k(l2)=mg+T1cos 30∘+T2cos 60∘
or √3T1+T2=kl−2mg.......(2)
Substituting value of T1 from equation (1) in equation (2) we get,
4T2=kl−2mg
T2=14(kl−2mg)
From equation (1), we have
T1=√34(kl−2mg)
As the natural length of spring is l, and in the situation shown in figure its length is 3l2. Thus the spring is stretched by a distance l2 hence it exerts a restoring force on block k(l2) upward as shown in figure, which shows also the tensions acting on the block along the directions of the strings. As the block is in equilibrium, we can balance all the forces acting on it along horizontal and vertical directions.
Along horizontal direction
T1 sin 30∘ =T2 sin 60∘
or T1=√3T2.......(1)
Along vertical direction
k(l2)=mg+T1cos 30∘+T2cos 60∘
or √3T1+T2=kl−2mg.......(2)
Substituting value of T1 from equation (1) in equation (2) we get,
4T2=kl−2mg
T2=14(kl−2mg)
From equation (1), we have
T1=√34(kl−2mg)
Suggest Corrections
0
Similar questions
