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A block B of mass m is suspended from a cord of length l attached to a cart A of mass m as shown in figure. The horizontal surface on which the cart moves is smooth.Initially both the cart and the block are at rest in the position shown, and then B is released. m=2 kg, angle = 45, g=10 1.find the acceleration of the cart immediately after the system is released .. a) 1/(root 2) b) 10/3 c) 10/(3 root 2) d) 5 2. find the magnitude of acceleration of B with respect to the cart immediately after the system is released.. answer-- 40/(3 root 2). please solve both questions ONLY inertial frame please.....

A block B of mass m is suspended from a cord of length l attached to a cart A of mass m as shown in figure. The horizontal surface  on which the cart moves is smooth.Initially both the cart and the block are at rest in the position shown, and then B is released.  m=2 kg, angle = 45,
g=10
1.find the acceleration of the cart immediately after the system is released ..
a) 1/(root 2)   b) 10/3  c) 10/(3 root 2)  d) 5
2. find the magnitude of acceleration of B with respect to the cart immediately after the system is released..
answer--    40/(3 root 2).
please solve both questions ONLY inertial frame please.....
 

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Grade:11

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
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Let the acceleration of block with respect to cart beA_rand that of cart beAbackwards. Hence the net acceleration of block is the vector sum of the two accelerations.
Writing equations for the accelerations in horizontal and vertical directions-

Tsin\theta=m(A_rcos\theta-A)
mg-Tcos\theta=m(A_r sin\theta)

Also since no external force acts on the system in vertical direction, the acceleration of center of mass in horizontal direction will be zero.


Solving the three equations gives

A=\dfrac{g}{3}; A_r=\dfrac{2\sqrt{2}g}{3}

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