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A block of mass m1 = 4kg lying on a plane inclined at an angle of 300, is connected to another freely suspended block of mass m2 = 6kg with the help of a string passing over a smooth pulley as shown in the figure. The acceleration of each block is (g =10 m/s2)?
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A block of mass m1 = 4kg lying on a plane inclined at an angle of 300,...
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A block of mass m1 = 4kg lying on a plane inclined at an angle of 300,...

Free Body Diagram
- For block m1:
- Tension force T acts upwards
- Component of weight m1gsin30 acts down the incline
- Normal force N acts perpendicular to the incline
- For block m2:
- Tension force T acts upwards
- Weight m2g acts downwards

Equations of Motion
- For block m1:
- m1gsin30 - T = m1a
- For block m2:
- T - m2g = m2a

Solving Equations
- Substitute T from the second equation into the first equation:
- m1gsin30 - (m2g - m2a) = m1a
- Simplify: m1gsin30 - m2g + m2a = m1a
- Rearrange: a(m1 + m2) = m1gsin30 - m2g
- Plug in values: a(4 + 6) = 4*10*sin30 - 6*10
- Solve for acceleration a

Calculation
- Substitute values and solve:
- a(10) = 40 - 60
- a(10) = -20
- a = -2 m/s^2

The acceleration of block m1 is -2 m/s^2 up the incline, while the acceleration of block m2 is 2 m/s^2 downwards. The negative sign indicates that the block m1 is moving up the incline, opposite to the assumed positive direction.
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A block of mass m1 = 4kg lying on a plane inclined at an angle of 300, is connected to another freely suspended block of mass m2 = 6kg with the help of a string passing over a smooth pulley as shown in the figure. The acceleration of each block is (g =10 m/s2)?
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