03. Forces in Mechanism
Laws of Motion

146069 A body of mass \(20 \mathrm{~kg}\) is moving on a rough horizontal plane. A block of mass \(3 \mathrm{~kg}\) is connected to the \(20 \mathrm{~kg}\) mass by a string of negligible mass through a smooth pulley as shown in the figure. The tension in the string is \(27 \mathrm{~N}\). The coefficient of kinetic friction between the heavier mass and the surface is \((g=10\) \(\mathbf{m} / \mathbf{s}^{2}\) )

1 0.025
2 0.035
3 0.35
4 0.25
Laws of Motion

146070 The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be

1 \(45^{\circ}\)
2 \(60^{\circ}\)
3 \(75^{\circ}\)
4 \(90^{\circ}\)
Laws of Motion

146071 Two weights \(w_{1}\) and \(w_{2}\) are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an acceleration \(g\), then the tension in the string is:

1 \(\frac{4 w_{1} w_{2}}{w_{1}+w_{2}}\)
2 \(\frac{w_{1} w_{2}}{w_{1}+w_{2}}\)
3 \(\frac{2 w_{1} w_{2}}{w_{1}+w_{2}}\)
4 \(\frac{\mathrm{w}_{1}+\mathrm{w}_{2}}{2}\)
For \(20 \mathrm{~kg}\) block,
Laws of Motion

146073 A block of mass \(M\) is pulled along a horizontal frictionless surface by a rope of mass \(\mathrm{m}\). If a force \(P\) is applied at the free end of the rope, the force exerted by the rope on the block is

1 \(\frac{P M}{(M+m)}\)
2 \(\frac{P M}{(M-m)}\)
3 \(\mathrm{P}\)
4 \(\frac{P M}{(M-m)}\)
Laws of Motion

146074 In the given figure the pulley is assumed mass less and frictionless. If the friction on the object of mass \(m\) is \(f\), then its acceleration in terms of the force \(F\) will be equal to

1 \((\mathrm{F}-\mathrm{f}) / \mathrm{m}\)
2 \(\left(\frac{\mathrm{F}}{2}-\mathrm{f}\right) / \mathrm{m}\)
3 \(\mathrm{F} / \mathrm{m}\)
4 None of these
Laws of Motion

146069 A body of mass \(20 \mathrm{~kg}\) is moving on a rough horizontal plane. A block of mass \(3 \mathrm{~kg}\) is connected to the \(20 \mathrm{~kg}\) mass by a string of negligible mass through a smooth pulley as shown in the figure. The tension in the string is \(27 \mathrm{~N}\). The coefficient of kinetic friction between the heavier mass and the surface is \((g=10\) \(\mathbf{m} / \mathbf{s}^{2}\) )

1 0.025
2 0.035
3 0.35
4 0.25
Laws of Motion

146070 The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be

1 \(45^{\circ}\)
2 \(60^{\circ}\)
3 \(75^{\circ}\)
4 \(90^{\circ}\)
Laws of Motion

146071 Two weights \(w_{1}\) and \(w_{2}\) are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an acceleration \(g\), then the tension in the string is:

1 \(\frac{4 w_{1} w_{2}}{w_{1}+w_{2}}\)
2 \(\frac{w_{1} w_{2}}{w_{1}+w_{2}}\)
3 \(\frac{2 w_{1} w_{2}}{w_{1}+w_{2}}\)
4 \(\frac{\mathrm{w}_{1}+\mathrm{w}_{2}}{2}\)
For \(20 \mathrm{~kg}\) block,
Laws of Motion

146073 A block of mass \(M\) is pulled along a horizontal frictionless surface by a rope of mass \(\mathrm{m}\). If a force \(P\) is applied at the free end of the rope, the force exerted by the rope on the block is

1 \(\frac{P M}{(M+m)}\)
2 \(\frac{P M}{(M-m)}\)
3 \(\mathrm{P}\)
4 \(\frac{P M}{(M-m)}\)
Laws of Motion

146074 In the given figure the pulley is assumed mass less and frictionless. If the friction on the object of mass \(m\) is \(f\), then its acceleration in terms of the force \(F\) will be equal to

1 \((\mathrm{F}-\mathrm{f}) / \mathrm{m}\)
2 \(\left(\frac{\mathrm{F}}{2}-\mathrm{f}\right) / \mathrm{m}\)
3 \(\mathrm{F} / \mathrm{m}\)
4 None of these
Laws of Motion

146069 A body of mass \(20 \mathrm{~kg}\) is moving on a rough horizontal plane. A block of mass \(3 \mathrm{~kg}\) is connected to the \(20 \mathrm{~kg}\) mass by a string of negligible mass through a smooth pulley as shown in the figure. The tension in the string is \(27 \mathrm{~N}\). The coefficient of kinetic friction between the heavier mass and the surface is \((g=10\) \(\mathbf{m} / \mathbf{s}^{2}\) )

1 0.025
2 0.035
3 0.35
4 0.25
Laws of Motion

146070 The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be

1 \(45^{\circ}\)
2 \(60^{\circ}\)
3 \(75^{\circ}\)
4 \(90^{\circ}\)
Laws of Motion

146071 Two weights \(w_{1}\) and \(w_{2}\) are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an acceleration \(g\), then the tension in the string is:

1 \(\frac{4 w_{1} w_{2}}{w_{1}+w_{2}}\)
2 \(\frac{w_{1} w_{2}}{w_{1}+w_{2}}\)
3 \(\frac{2 w_{1} w_{2}}{w_{1}+w_{2}}\)
4 \(\frac{\mathrm{w}_{1}+\mathrm{w}_{2}}{2}\)
For \(20 \mathrm{~kg}\) block,
Laws of Motion

146073 A block of mass \(M\) is pulled along a horizontal frictionless surface by a rope of mass \(\mathrm{m}\). If a force \(P\) is applied at the free end of the rope, the force exerted by the rope on the block is

1 \(\frac{P M}{(M+m)}\)
2 \(\frac{P M}{(M-m)}\)
3 \(\mathrm{P}\)
4 \(\frac{P M}{(M-m)}\)
Laws of Motion

146074 In the given figure the pulley is assumed mass less and frictionless. If the friction on the object of mass \(m\) is \(f\), then its acceleration in terms of the force \(F\) will be equal to

1 \((\mathrm{F}-\mathrm{f}) / \mathrm{m}\)
2 \(\left(\frac{\mathrm{F}}{2}-\mathrm{f}\right) / \mathrm{m}\)
3 \(\mathrm{F} / \mathrm{m}\)
4 None of these
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Laws of Motion

146069 A body of mass \(20 \mathrm{~kg}\) is moving on a rough horizontal plane. A block of mass \(3 \mathrm{~kg}\) is connected to the \(20 \mathrm{~kg}\) mass by a string of negligible mass through a smooth pulley as shown in the figure. The tension in the string is \(27 \mathrm{~N}\). The coefficient of kinetic friction between the heavier mass and the surface is \((g=10\) \(\mathbf{m} / \mathbf{s}^{2}\) )

1 0.025
2 0.035
3 0.35
4 0.25
Laws of Motion

146070 The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be

1 \(45^{\circ}\)
2 \(60^{\circ}\)
3 \(75^{\circ}\)
4 \(90^{\circ}\)
Laws of Motion

146071 Two weights \(w_{1}\) and \(w_{2}\) are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an acceleration \(g\), then the tension in the string is:

1 \(\frac{4 w_{1} w_{2}}{w_{1}+w_{2}}\)
2 \(\frac{w_{1} w_{2}}{w_{1}+w_{2}}\)
3 \(\frac{2 w_{1} w_{2}}{w_{1}+w_{2}}\)
4 \(\frac{\mathrm{w}_{1}+\mathrm{w}_{2}}{2}\)
For \(20 \mathrm{~kg}\) block,
Laws of Motion

146073 A block of mass \(M\) is pulled along a horizontal frictionless surface by a rope of mass \(\mathrm{m}\). If a force \(P\) is applied at the free end of the rope, the force exerted by the rope on the block is

1 \(\frac{P M}{(M+m)}\)
2 \(\frac{P M}{(M-m)}\)
3 \(\mathrm{P}\)
4 \(\frac{P M}{(M-m)}\)
Laws of Motion

146074 In the given figure the pulley is assumed mass less and frictionless. If the friction on the object of mass \(m\) is \(f\), then its acceleration in terms of the force \(F\) will be equal to

1 \((\mathrm{F}-\mathrm{f}) / \mathrm{m}\)
2 \(\left(\frac{\mathrm{F}}{2}-\mathrm{f}\right) / \mathrm{m}\)
3 \(\mathrm{F} / \mathrm{m}\)
4 None of these
Laws of Motion

146069 A body of mass \(20 \mathrm{~kg}\) is moving on a rough horizontal plane. A block of mass \(3 \mathrm{~kg}\) is connected to the \(20 \mathrm{~kg}\) mass by a string of negligible mass through a smooth pulley as shown in the figure. The tension in the string is \(27 \mathrm{~N}\). The coefficient of kinetic friction between the heavier mass and the surface is \((g=10\) \(\mathbf{m} / \mathbf{s}^{2}\) )

1 0.025
2 0.035
3 0.35
4 0.25
Laws of Motion

146070 The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be

1 \(45^{\circ}\)
2 \(60^{\circ}\)
3 \(75^{\circ}\)
4 \(90^{\circ}\)
Laws of Motion

146071 Two weights \(w_{1}\) and \(w_{2}\) are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an acceleration \(g\), then the tension in the string is:

1 \(\frac{4 w_{1} w_{2}}{w_{1}+w_{2}}\)
2 \(\frac{w_{1} w_{2}}{w_{1}+w_{2}}\)
3 \(\frac{2 w_{1} w_{2}}{w_{1}+w_{2}}\)
4 \(\frac{\mathrm{w}_{1}+\mathrm{w}_{2}}{2}\)
For \(20 \mathrm{~kg}\) block,
Laws of Motion

146073 A block of mass \(M\) is pulled along a horizontal frictionless surface by a rope of mass \(\mathrm{m}\). If a force \(P\) is applied at the free end of the rope, the force exerted by the rope on the block is

1 \(\frac{P M}{(M+m)}\)
2 \(\frac{P M}{(M-m)}\)
3 \(\mathrm{P}\)
4 \(\frac{P M}{(M-m)}\)
Laws of Motion

146074 In the given figure the pulley is assumed mass less and frictionless. If the friction on the object of mass \(m\) is \(f\), then its acceleration in terms of the force \(F\) will be equal to

1 \((\mathrm{F}-\mathrm{f}) / \mathrm{m}\)
2 \(\left(\frac{\mathrm{F}}{2}-\mathrm{f}\right) / \mathrm{m}\)
3 \(\mathrm{F} / \mathrm{m}\)
4 None of these