This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the forces acting on body P. The body P is in equilibrium, meaning the net force acting on it is zero. The forces acting on body P are: • The weight of the body (W) acting vertically downwards. • The tension (T) in the string, acting upwards and to the right at an angle of 60^ to the horizontal. • A horizontal force (F) acting to the left. Step 2: Calculate the weight of the body. Given mass m = 10 \, kg and acceleration due to gravity g = 10 \, m/s^2. W = mg W = 10 \, kg × 10 \, m/s^2 W = 100 \, N Step 3: Resolve the tension force into its vertical and horizontal components. The tension T acts at an angle of 60^ to the horizontal. • Vertical component of tension: T_y = T (60^) (upwards) • Horizontal component of tension: T_x = T (60^) (to the right) Step 4: Apply the condition for vertical equilibrium. Since the body is in equilibrium, the sum of vertical forces must be zero. The upward vertical component of tension must balance the downward weight. F_y = 0 T (60^) - W = 0 T (60^) = W Step 5: Solve for the tension T. Substitute the value of W and (60^). (60^) = sqrt(3)2 T (sqrt(3)2) = 100 \, N T = 100 \, Nsqrt(3)2 T = (200)/(sqrt(3)) \, N To rationalize the denominator, multiply the numerator and denominator by sqrt(3): T = 200 sqrt(3)3 \, N Using sqrt(3) ≈ 1.732: T ≈ (200 × 1.732)/(3) \, N T ≈ (346.4)/(3) \, N T ≈ 115.47 \, N The tension in the string is 115.47 N.