Normal force on B by the floor = F       Force exerted by block A on B:  F1         F - m_B g -  F1 = - m_B * 2        =>  F = F1 + m_B g - 2 m_B         F1 - m_A  g = - m_A * 2            =>  F1 = g/2 - 1  = 4  Newtons             =======================9.  component of weight/acceleration due to gravity along the inclined slope             = g Sin 30 = g/2      Component of weight/acceleration along the groove OA = g/2 Sin 30 = g/4     s = u t + 1/2 a t²    => t² = 2 s / a               t² = 2 * 5 /  (g/4) = 4              =>           t = 2 sec.=================10.      m1 = 100 kg          M2 = 60 kg  a1 = acceleration of 100 kg upwards.  Rope is also moving with the same acceleration.       T - 100 kg * g = 100 kg * a1        => T = 1000+ 100 a1          ---- (1)          Acceleration of the person = a     relative acceleration of the man wrt rope  = a + a1  = 5g/4              => a = 5g/4 - a1  = 12.5 - a1      upwards     T - 60 kg * g = 60 kg * a       T = 600 + 60 a = 600 + 60 (12.5 - a1) = 1350 - 60 a1      ----- (2)       Solving the two equations          a1 = 350/160  m/sec/sec       T = 1000 + 100 * 35/16 = 1218  N======================11         F = buoyancy force upwards  remains same         F - M g  = M a        => F = M (g+a)         F - (M-m) g = (M-m) a'          =>  a' = [ M g + Ma - Mg + mg ] / (M-m)                 a' = (M a + m g)/(M-m)===============================12.        T - 5 g = 5 a             10 g - T = 10 a            a = g/3=================   13.      F - m g Sin 37  = m a          along the slope           5.5 - 0.50 * g * 0.6  = 0.50 a      =>  a = 5 m/sec/sec                         v^2 = 2 a s = 2 * 5 * 10  = 100              v = 10 m/s    at the TOP of the incline.         ANGLE of projection = 37 deg.             y initial = 10 Sin 37 = 6 meters           Time to REACH the top point :    u Sin 37 / g = 10 * 0.6 / 10 = 0.60 sec           height reached = s  =  u sin 37 * 0.60 - 1/2 * 10 * 0.60^2                                         = 10  * 0.6 * 0.60 - 5 * 0.60^2  = 1.80 meters           total height at the top of the flight = 6 + 1.80 = 7.80 m           time to reach the ground = t  => t^2 = 2s / g =>        t = 2 * 7.80 / 10 = 1.56 sec       total time of the flight = 2.16 sec.          total  horizontal distance travelled after projection from the ramp                   =  u cos 37 * 1.56 sec                    = 12.48 meters