Three blocks are connected as shown in fig. on a horizontal frictionless table if M1 = 1 kg, M2 = 8 kg, M3 = 27 kg and T3 = 36N, T2 will be :-

To find the value of T2, we can use Newton's second law of motion and consider the forces acting on each block.

1. Start by analyzing the forces acting on block M1. The only force acting on it is T1, which is the tension in the string connecting M1 and M2. Since the table is frictionless, there is no friction force.

2. According to Newton's second law, the net force on M1 is equal to its mass multiplied by its acceleration. Since M1 is not accelerating vertically, the net force in the vertical direction is zero. Therefore, the tension T1 is equal to the weight of M1, which is given by T1 = M1 * g, where g is the acceleration due to gravity.

3. Now, let's consider the forces acting on block M2. The tension T1 is acting upwards, and the tension T2 is acting downwards. Additionally, the weight of M2 is acting downwards. Since M2 is not accelerating vertically, the net force in the vertical direction is zero. Therefore, the sum of the downward forces (T2 + M2 * g) must be equal to the sum of the upward forces (T1).

4. We can now substitute the value of T1 from step 2 into the equation from step 3. This gives us T2 + M2 * g = T1 = M1 * g.

5. Substitute the given values into the equation. M1 = 1 kg, M2 = 8 kg, and g is approximately 9.8 m/s^2.

T2 + 8 kg * 9.8 m/s^2 = 1 kg * 9.8 m/s^2.

6. Solve the equation for T2. Subtracting 8 kg * 9.8 m/s^2 from both sides gives us:

T2 = 1 kg * 9.8 m/s^2 - 8 kg * 9.8 m/s^2.

T2 = 9.8 m/s^2 - 78.4 m/s^2.

T2 = -68.6 m/s^2.

Therefore, T2 is equal to -68.6 N.