EQUILIBRIUM OF A PARTICLE
Laws of Motion

270162 A mass of \(10 \mathrm{~kg}\) is suspended by a rope of length \(2.8 \mathrm{~m}\) from a ceiling. A force of \(98 \mathrm{~N}\) is applied at the midpoint of the rope as shown in figure. The angle which the rope makes with the vertical in equilibrium is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(45^{\circ}\)
4 \(90^{\circ}\)
Laws of Motion

270163 A mass of \(M \mathrm{~kg}\) is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle \(45^{\circ}\) with the initial vertical direction is

1 \(M g\)
2 \(\frac{M g}{\sqrt{2}}\)
3 \(\operatorname{Mg}(\sqrt{2}+1)\)
4 \(\sqrt{2} \mathrm{Mg}\)
Laws of Motion

270267 Two masses \(M_{1}\) and \(M_{2}\) connected by means of a string which is made to pass over light, smooth pulley are in equilibrium on a fixed smooth wedge as shown in figure. If\(\theta=60^{\circ}\) and \(\alpha=30^{\circ}\), then the ratio of \(M_{1}\) to \(M_{2}\) is

1 \(1: 2\)
2 \(2: \sqrt{3}\)
3 \(1: \sqrt{3}\)
4 \(\sqrt{3}: 1\)
Laws of Motion

270268 If '\(O\) ' is at equilibrium then the values of the tension \(T_{1}\) and \(T_{2}\) respectively.

1 \(20 \mathrm{~N}, 30 \mathrm{~N}\)
2 \(20 \sqrt{3} \mathrm{~N}, 20 \mathrm{~N}\)
3 \(20 \sqrt{3} \mathrm{~N}, 20 \sqrt{3} \mathrm{~N}\)
4 \(10 \mathrm{~N}, 30 \mathrm{~N}\)
Laws of Motion

270269 A\(1 \mathrm{~N}\) pendulum bob is held at an angle \(\theta\) from the vertical by a \(2 \mathrm{~N}\) horizontal force \(F\) as shown in the figure. The tension in the string supporting the pendulum bob (in newton) is
(2011E )

1 \(\cos \theta\)
2 \(\frac{2}{\cos \theta}\)
3 \(\sqrt{5}\)
4 1
Laws of Motion

270162 A mass of \(10 \mathrm{~kg}\) is suspended by a rope of length \(2.8 \mathrm{~m}\) from a ceiling. A force of \(98 \mathrm{~N}\) is applied at the midpoint of the rope as shown in figure. The angle which the rope makes with the vertical in equilibrium is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(45^{\circ}\)
4 \(90^{\circ}\)
Laws of Motion

270163 A mass of \(M \mathrm{~kg}\) is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle \(45^{\circ}\) with the initial vertical direction is

1 \(M g\)
2 \(\frac{M g}{\sqrt{2}}\)
3 \(\operatorname{Mg}(\sqrt{2}+1)\)
4 \(\sqrt{2} \mathrm{Mg}\)
Laws of Motion

270267 Two masses \(M_{1}\) and \(M_{2}\) connected by means of a string which is made to pass over light, smooth pulley are in equilibrium on a fixed smooth wedge as shown in figure. If\(\theta=60^{\circ}\) and \(\alpha=30^{\circ}\), then the ratio of \(M_{1}\) to \(M_{2}\) is

1 \(1: 2\)
2 \(2: \sqrt{3}\)
3 \(1: \sqrt{3}\)
4 \(\sqrt{3}: 1\)
Laws of Motion

270268 If '\(O\) ' is at equilibrium then the values of the tension \(T_{1}\) and \(T_{2}\) respectively.

1 \(20 \mathrm{~N}, 30 \mathrm{~N}\)
2 \(20 \sqrt{3} \mathrm{~N}, 20 \mathrm{~N}\)
3 \(20 \sqrt{3} \mathrm{~N}, 20 \sqrt{3} \mathrm{~N}\)
4 \(10 \mathrm{~N}, 30 \mathrm{~N}\)
Laws of Motion

270269 A\(1 \mathrm{~N}\) pendulum bob is held at an angle \(\theta\) from the vertical by a \(2 \mathrm{~N}\) horizontal force \(F\) as shown in the figure. The tension in the string supporting the pendulum bob (in newton) is
(2011E )

1 \(\cos \theta\)
2 \(\frac{2}{\cos \theta}\)
3 \(\sqrt{5}\)
4 1
Laws of Motion

270162 A mass of \(10 \mathrm{~kg}\) is suspended by a rope of length \(2.8 \mathrm{~m}\) from a ceiling. A force of \(98 \mathrm{~N}\) is applied at the midpoint of the rope as shown in figure. The angle which the rope makes with the vertical in equilibrium is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(45^{\circ}\)
4 \(90^{\circ}\)
Laws of Motion

270163 A mass of \(M \mathrm{~kg}\) is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle \(45^{\circ}\) with the initial vertical direction is

1 \(M g\)
2 \(\frac{M g}{\sqrt{2}}\)
3 \(\operatorname{Mg}(\sqrt{2}+1)\)
4 \(\sqrt{2} \mathrm{Mg}\)
Laws of Motion

270267 Two masses \(M_{1}\) and \(M_{2}\) connected by means of a string which is made to pass over light, smooth pulley are in equilibrium on a fixed smooth wedge as shown in figure. If\(\theta=60^{\circ}\) and \(\alpha=30^{\circ}\), then the ratio of \(M_{1}\) to \(M_{2}\) is

1 \(1: 2\)
2 \(2: \sqrt{3}\)
3 \(1: \sqrt{3}\)
4 \(\sqrt{3}: 1\)
Laws of Motion

270268 If '\(O\) ' is at equilibrium then the values of the tension \(T_{1}\) and \(T_{2}\) respectively.

1 \(20 \mathrm{~N}, 30 \mathrm{~N}\)
2 \(20 \sqrt{3} \mathrm{~N}, 20 \mathrm{~N}\)
3 \(20 \sqrt{3} \mathrm{~N}, 20 \sqrt{3} \mathrm{~N}\)
4 \(10 \mathrm{~N}, 30 \mathrm{~N}\)
Laws of Motion

270269 A\(1 \mathrm{~N}\) pendulum bob is held at an angle \(\theta\) from the vertical by a \(2 \mathrm{~N}\) horizontal force \(F\) as shown in the figure. The tension in the string supporting the pendulum bob (in newton) is
(2011E )

1 \(\cos \theta\)
2 \(\frac{2}{\cos \theta}\)
3 \(\sqrt{5}\)
4 1
Laws of Motion

270162 A mass of \(10 \mathrm{~kg}\) is suspended by a rope of length \(2.8 \mathrm{~m}\) from a ceiling. A force of \(98 \mathrm{~N}\) is applied at the midpoint of the rope as shown in figure. The angle which the rope makes with the vertical in equilibrium is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(45^{\circ}\)
4 \(90^{\circ}\)
Laws of Motion

270163 A mass of \(M \mathrm{~kg}\) is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle \(45^{\circ}\) with the initial vertical direction is

1 \(M g\)
2 \(\frac{M g}{\sqrt{2}}\)
3 \(\operatorname{Mg}(\sqrt{2}+1)\)
4 \(\sqrt{2} \mathrm{Mg}\)
Laws of Motion

270267 Two masses \(M_{1}\) and \(M_{2}\) connected by means of a string which is made to pass over light, smooth pulley are in equilibrium on a fixed smooth wedge as shown in figure. If\(\theta=60^{\circ}\) and \(\alpha=30^{\circ}\), then the ratio of \(M_{1}\) to \(M_{2}\) is

1 \(1: 2\)
2 \(2: \sqrt{3}\)
3 \(1: \sqrt{3}\)
4 \(\sqrt{3}: 1\)
Laws of Motion

270268 If '\(O\) ' is at equilibrium then the values of the tension \(T_{1}\) and \(T_{2}\) respectively.

1 \(20 \mathrm{~N}, 30 \mathrm{~N}\)
2 \(20 \sqrt{3} \mathrm{~N}, 20 \mathrm{~N}\)
3 \(20 \sqrt{3} \mathrm{~N}, 20 \sqrt{3} \mathrm{~N}\)
4 \(10 \mathrm{~N}, 30 \mathrm{~N}\)
Laws of Motion

270269 A\(1 \mathrm{~N}\) pendulum bob is held at an angle \(\theta\) from the vertical by a \(2 \mathrm{~N}\) horizontal force \(F\) as shown in the figure. The tension in the string supporting the pendulum bob (in newton) is
(2011E )

1 \(\cos \theta\)
2 \(\frac{2}{\cos \theta}\)
3 \(\sqrt{5}\)
4 1
Laws of Motion

270162 A mass of \(10 \mathrm{~kg}\) is suspended by a rope of length \(2.8 \mathrm{~m}\) from a ceiling. A force of \(98 \mathrm{~N}\) is applied at the midpoint of the rope as shown in figure. The angle which the rope makes with the vertical in equilibrium is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(45^{\circ}\)
4 \(90^{\circ}\)
Laws of Motion

270163 A mass of \(M \mathrm{~kg}\) is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle \(45^{\circ}\) with the initial vertical direction is

1 \(M g\)
2 \(\frac{M g}{\sqrt{2}}\)
3 \(\operatorname{Mg}(\sqrt{2}+1)\)
4 \(\sqrt{2} \mathrm{Mg}\)
Laws of Motion

270267 Two masses \(M_{1}\) and \(M_{2}\) connected by means of a string which is made to pass over light, smooth pulley are in equilibrium on a fixed smooth wedge as shown in figure. If\(\theta=60^{\circ}\) and \(\alpha=30^{\circ}\), then the ratio of \(M_{1}\) to \(M_{2}\) is

1 \(1: 2\)
2 \(2: \sqrt{3}\)
3 \(1: \sqrt{3}\)
4 \(\sqrt{3}: 1\)
Laws of Motion

270268 If '\(O\) ' is at equilibrium then the values of the tension \(T_{1}\) and \(T_{2}\) respectively.

1 \(20 \mathrm{~N}, 30 \mathrm{~N}\)
2 \(20 \sqrt{3} \mathrm{~N}, 20 \mathrm{~N}\)
3 \(20 \sqrt{3} \mathrm{~N}, 20 \sqrt{3} \mathrm{~N}\)
4 \(10 \mathrm{~N}, 30 \mathrm{~N}\)
Laws of Motion

270269 A\(1 \mathrm{~N}\) pendulum bob is held at an angle \(\theta\) from the vertical by a \(2 \mathrm{~N}\) horizontal force \(F\) as shown in the figure. The tension in the string supporting the pendulum bob (in newton) is
(2011E )

1 \(\cos \theta\)
2 \(\frac{2}{\cos \theta}\)
3 \(\sqrt{5}\)
4 1