Four blocks (A, B, C ) and (D ) of masses (6 ~kg , 3 ~kg ), (6 ~kg ) and ( I kg ) respectively are connected by light strings passing over frictionless pulleys as shown in the figure. The strings (P ) and (Q ) are horizontal. The coefficient of friction between the horizontal surface and the block (B ) is 0.2 and the blocks (A ) and (B ) move together. If the system is released from rest then the tension in the strin

Step-by-step solution

Given, (m_A=6 ~kg , m_B=3 ~kg , m_C=6 ~kg ), and (m_D=1 ~kg ) and coefficient of friction between block (B ) and horizontal surface, ( =0.2 ) Now, the acceleration of complete system, ( aligned a & = m_C g-m_D g- (m_A+m_B ) g m_A+m_B+m_C+m_D & = 6 10-1 10-0.2(6+3) 10 6+3+6+1 & = 60-10-18 16 & = 32 16 =2 ~ms ⁻² aligned ) Now, the tension in the string (Q ) is given by ( aligned m_D a & =T-m_D g T & =m_D a+m_D g T & =1 2+1 10=12 ~N aligned ) Hence, the correct answer is (c).