Consider two blocks A and B of masses \( m_1 = 10 \) kg and \( m_2 = 5 \) kg that are placed on a frictionless table. The block A moves with a constant speed \( v = 3 \) m/s towards the block B kept at rest. A spring with spring constant \( k = 3000 \) N/m is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)
If the ratio of the terms equidistant from the middle term in the expansion of \((1 + x)^{12}\) is \(\frac{1}{256}\), then the sum of all the terms of the expansion \((1 + x)^{12}\) is:
A 3 kg block is connected as shown in the figure. Spring constants of two springs \( K_1 \) and \( K_2 \) are 50 Nm\(^{-1}\) and 150 Nm\(^{-1}\) respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is ( \( g = 10 \) ms\(^{-2}\) )