1.

A pendulum is hanging from the ceiling of a cage T1, T2 are the tensions in the string. When the cage is moving upward and downward with same acceleration. What is the tension in the string if is move horizontaly? (solve in IIT method).

Answer»

Final ANSWER :
T = \sqrt{\frac{T_1^2+T_2^2}{2}}

Steps:
1) Let the acceleration be 'a' in all cases.
We got,
When acceleration is downward,
mg-T_2=ma \\ => T_2 =m(g-a) --(1)

2) When acceleration is upward ,
T_1 -mg = ma \\ => T_1 = m(g+a) --(2)

3) When acceleration is horizontal,
T \sin(\theta) = ma \\ T \cos(\theta) = mg \\ => T^2 = (mg)^2 + (ma)^2 \\ => T = m \sqrt{g^2 + a^2 }

4) Squaring EQ. (1) and (2) :
T_1^2 + T_2^2 = 2m^2( a^2 + g^2) \\ => T_1^2+ T_2^2 = 2T^2 \\ => T = \sqrt{\frac{T_1^2+T_2^2}{2}}
Hope , you got desired answer.


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