Forces in Mechanism
LAWS OF MOTION (ADDITIONAL)

371876 A cyclist leans with the horizontal at angle \(30^{\circ}\), while negotiating round a circular road of radius \(20 \sqrt{3} \mathrm{~m}\). The speed of the cycle should be

1 \(7 \sqrt{3} \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(7 \sqrt{6} \mathrm{~m} / \mathrm{s}\)
4 \(10 \sqrt{6} \mathrm{~m} / \mathrm{s}\)
LAWS OF MOTION (ADDITIONAL)

371877 A mass \(m\) is supported by a massless string wound around a uniform hollow cylinder of mass \(m\) and radius \(R\). If the string does not slip on the cylinder, then with what acceleration will the mass release?
(Assume, \(g\) = acceleration due to gravity)

1 \(\frac{2 g}{3}\)
2 \(\frac{g}{2}\)
3 \(\frac{5 \mathrm{~g}}{6}\)
4 \(g\)
LAWS OF MOTION (ADDITIONAL)

371878 An infinite number of masses are placed on a frictionless table and they are connected via mass less strings. Their masses follow the sequence, \(m, \frac{m}{2}, \frac{m}{6}, \ldots \ldots \ldots . . . \frac{m}{n !}\), and they are further connected to a mass \(m\) that hangs over a mass less pulley. The acceleration of the hanging mass is

1 \(\frac{\mathrm{g}}{\mathrm{e}-1}\)
2 \(\frac{g}{e+1}\)
3 \(\frac{\mathrm{g}}{\mathrm{e}}\)
4 \(\frac{\mathrm{g}}{2 \mathrm{e}}\)
LAWS OF MOTION (ADDITIONAL)

371879 Three blocks of masses \(2 \mathrm{~kg} .1 \mathrm{~kg}\) and \(0.5 \mathrm{~kg}\) are connected by an inextensible string as shown below. A below of \(10 \mathrm{~N}\) is applied on the body of mass \(2 \mathrm{~kg}\). The acceleration of the system and the tensions \(T_{1}\) and \(T_{2}\) are

1 \(2.86 \mathrm{~ms}^{-2}, 4.29 \mathrm{~N}, 1.43 \mathrm{~N}\)
2 \(3.00 \mathrm{~ms}^{-2}, 5.00 \mathrm{~N}, 6.20 \mathrm{~N}\)
3 \(7.25 \mathrm{~ms}^{-2}, 2.35 \mathrm{~N}, 3.15 \mathrm{~N}\)
4 \(2.00 \mathrm{~ms}^{-2}, 4.32 \mathrm{~N}, 8.64 \mathrm{~N}\)
LAWS OF MOTION (ADDITIONAL)

371880 In the arrangement shown in the figure, work done by the string on the block of mass \(0.36 \mathrm{~kg}\) during the first second after the blocks are released from state of rest is (Ignore friction and mass of the string.)
(Acceleration due to gravity, \(\mathrm{g}=\mathbf{1 0} \mathbf{~ m s}^{-2}\) )

1 \(8 \mathrm{~J}\)
2 \(4 \mathrm{~J}\)
3 \(12 \mathrm{~J}\)
4 \(2 \mathrm{~J}\)
LAWS OF MOTION (ADDITIONAL)

371876 A cyclist leans with the horizontal at angle \(30^{\circ}\), while negotiating round a circular road of radius \(20 \sqrt{3} \mathrm{~m}\). The speed of the cycle should be

1 \(7 \sqrt{3} \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(7 \sqrt{6} \mathrm{~m} / \mathrm{s}\)
4 \(10 \sqrt{6} \mathrm{~m} / \mathrm{s}\)
LAWS OF MOTION (ADDITIONAL)

371877 A mass \(m\) is supported by a massless string wound around a uniform hollow cylinder of mass \(m\) and radius \(R\). If the string does not slip on the cylinder, then with what acceleration will the mass release?
(Assume, \(g\) = acceleration due to gravity)

1 \(\frac{2 g}{3}\)
2 \(\frac{g}{2}\)
3 \(\frac{5 \mathrm{~g}}{6}\)
4 \(g\)
LAWS OF MOTION (ADDITIONAL)

371878 An infinite number of masses are placed on a frictionless table and they are connected via mass less strings. Their masses follow the sequence, \(m, \frac{m}{2}, \frac{m}{6}, \ldots \ldots \ldots . . . \frac{m}{n !}\), and they are further connected to a mass \(m\) that hangs over a mass less pulley. The acceleration of the hanging mass is

1 \(\frac{\mathrm{g}}{\mathrm{e}-1}\)
2 \(\frac{g}{e+1}\)
3 \(\frac{\mathrm{g}}{\mathrm{e}}\)
4 \(\frac{\mathrm{g}}{2 \mathrm{e}}\)
LAWS OF MOTION (ADDITIONAL)

371879 Three blocks of masses \(2 \mathrm{~kg} .1 \mathrm{~kg}\) and \(0.5 \mathrm{~kg}\) are connected by an inextensible string as shown below. A below of \(10 \mathrm{~N}\) is applied on the body of mass \(2 \mathrm{~kg}\). The acceleration of the system and the tensions \(T_{1}\) and \(T_{2}\) are

1 \(2.86 \mathrm{~ms}^{-2}, 4.29 \mathrm{~N}, 1.43 \mathrm{~N}\)
2 \(3.00 \mathrm{~ms}^{-2}, 5.00 \mathrm{~N}, 6.20 \mathrm{~N}\)
3 \(7.25 \mathrm{~ms}^{-2}, 2.35 \mathrm{~N}, 3.15 \mathrm{~N}\)
4 \(2.00 \mathrm{~ms}^{-2}, 4.32 \mathrm{~N}, 8.64 \mathrm{~N}\)
LAWS OF MOTION (ADDITIONAL)

371880 In the arrangement shown in the figure, work done by the string on the block of mass \(0.36 \mathrm{~kg}\) during the first second after the blocks are released from state of rest is (Ignore friction and mass of the string.)
(Acceleration due to gravity, \(\mathrm{g}=\mathbf{1 0} \mathbf{~ m s}^{-2}\) )

1 \(8 \mathrm{~J}\)
2 \(4 \mathrm{~J}\)
3 \(12 \mathrm{~J}\)
4 \(2 \mathrm{~J}\)
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LAWS OF MOTION (ADDITIONAL)

371876 A cyclist leans with the horizontal at angle \(30^{\circ}\), while negotiating round a circular road of radius \(20 \sqrt{3} \mathrm{~m}\). The speed of the cycle should be

1 \(7 \sqrt{3} \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(7 \sqrt{6} \mathrm{~m} / \mathrm{s}\)
4 \(10 \sqrt{6} \mathrm{~m} / \mathrm{s}\)
LAWS OF MOTION (ADDITIONAL)

371877 A mass \(m\) is supported by a massless string wound around a uniform hollow cylinder of mass \(m\) and radius \(R\). If the string does not slip on the cylinder, then with what acceleration will the mass release?
(Assume, \(g\) = acceleration due to gravity)

1 \(\frac{2 g}{3}\)
2 \(\frac{g}{2}\)
3 \(\frac{5 \mathrm{~g}}{6}\)
4 \(g\)
LAWS OF MOTION (ADDITIONAL)

371878 An infinite number of masses are placed on a frictionless table and they are connected via mass less strings. Their masses follow the sequence, \(m, \frac{m}{2}, \frac{m}{6}, \ldots \ldots \ldots . . . \frac{m}{n !}\), and they are further connected to a mass \(m\) that hangs over a mass less pulley. The acceleration of the hanging mass is

1 \(\frac{\mathrm{g}}{\mathrm{e}-1}\)
2 \(\frac{g}{e+1}\)
3 \(\frac{\mathrm{g}}{\mathrm{e}}\)
4 \(\frac{\mathrm{g}}{2 \mathrm{e}}\)
LAWS OF MOTION (ADDITIONAL)

371879 Three blocks of masses \(2 \mathrm{~kg} .1 \mathrm{~kg}\) and \(0.5 \mathrm{~kg}\) are connected by an inextensible string as shown below. A below of \(10 \mathrm{~N}\) is applied on the body of mass \(2 \mathrm{~kg}\). The acceleration of the system and the tensions \(T_{1}\) and \(T_{2}\) are

1 \(2.86 \mathrm{~ms}^{-2}, 4.29 \mathrm{~N}, 1.43 \mathrm{~N}\)
2 \(3.00 \mathrm{~ms}^{-2}, 5.00 \mathrm{~N}, 6.20 \mathrm{~N}\)
3 \(7.25 \mathrm{~ms}^{-2}, 2.35 \mathrm{~N}, 3.15 \mathrm{~N}\)
4 \(2.00 \mathrm{~ms}^{-2}, 4.32 \mathrm{~N}, 8.64 \mathrm{~N}\)
LAWS OF MOTION (ADDITIONAL)

371880 In the arrangement shown in the figure, work done by the string on the block of mass \(0.36 \mathrm{~kg}\) during the first second after the blocks are released from state of rest is (Ignore friction and mass of the string.)
(Acceleration due to gravity, \(\mathrm{g}=\mathbf{1 0} \mathbf{~ m s}^{-2}\) )

1 \(8 \mathrm{~J}\)
2 \(4 \mathrm{~J}\)
3 \(12 \mathrm{~J}\)
4 \(2 \mathrm{~J}\)
LAWS OF MOTION (ADDITIONAL)

371876 A cyclist leans with the horizontal at angle \(30^{\circ}\), while negotiating round a circular road of radius \(20 \sqrt{3} \mathrm{~m}\). The speed of the cycle should be

1 \(7 \sqrt{3} \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(7 \sqrt{6} \mathrm{~m} / \mathrm{s}\)
4 \(10 \sqrt{6} \mathrm{~m} / \mathrm{s}\)
LAWS OF MOTION (ADDITIONAL)

371877 A mass \(m\) is supported by a massless string wound around a uniform hollow cylinder of mass \(m\) and radius \(R\). If the string does not slip on the cylinder, then with what acceleration will the mass release?
(Assume, \(g\) = acceleration due to gravity)

1 \(\frac{2 g}{3}\)
2 \(\frac{g}{2}\)
3 \(\frac{5 \mathrm{~g}}{6}\)
4 \(g\)
LAWS OF MOTION (ADDITIONAL)

371878 An infinite number of masses are placed on a frictionless table and they are connected via mass less strings. Their masses follow the sequence, \(m, \frac{m}{2}, \frac{m}{6}, \ldots \ldots \ldots . . . \frac{m}{n !}\), and they are further connected to a mass \(m\) that hangs over a mass less pulley. The acceleration of the hanging mass is

1 \(\frac{\mathrm{g}}{\mathrm{e}-1}\)
2 \(\frac{g}{e+1}\)
3 \(\frac{\mathrm{g}}{\mathrm{e}}\)
4 \(\frac{\mathrm{g}}{2 \mathrm{e}}\)
LAWS OF MOTION (ADDITIONAL)

371879 Three blocks of masses \(2 \mathrm{~kg} .1 \mathrm{~kg}\) and \(0.5 \mathrm{~kg}\) are connected by an inextensible string as shown below. A below of \(10 \mathrm{~N}\) is applied on the body of mass \(2 \mathrm{~kg}\). The acceleration of the system and the tensions \(T_{1}\) and \(T_{2}\) are

1 \(2.86 \mathrm{~ms}^{-2}, 4.29 \mathrm{~N}, 1.43 \mathrm{~N}\)
2 \(3.00 \mathrm{~ms}^{-2}, 5.00 \mathrm{~N}, 6.20 \mathrm{~N}\)
3 \(7.25 \mathrm{~ms}^{-2}, 2.35 \mathrm{~N}, 3.15 \mathrm{~N}\)
4 \(2.00 \mathrm{~ms}^{-2}, 4.32 \mathrm{~N}, 8.64 \mathrm{~N}\)
LAWS OF MOTION (ADDITIONAL)

371880 In the arrangement shown in the figure, work done by the string on the block of mass \(0.36 \mathrm{~kg}\) during the first second after the blocks are released from state of rest is (Ignore friction and mass of the string.)
(Acceleration due to gravity, \(\mathrm{g}=\mathbf{1 0} \mathbf{~ m s}^{-2}\) )

1 \(8 \mathrm{~J}\)
2 \(4 \mathrm{~J}\)
3 \(12 \mathrm{~J}\)
4 \(2 \mathrm{~J}\)
LAWS OF MOTION (ADDITIONAL)

371876 A cyclist leans with the horizontal at angle \(30^{\circ}\), while negotiating round a circular road of radius \(20 \sqrt{3} \mathrm{~m}\). The speed of the cycle should be

1 \(7 \sqrt{3} \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(7 \sqrt{6} \mathrm{~m} / \mathrm{s}\)
4 \(10 \sqrt{6} \mathrm{~m} / \mathrm{s}\)
LAWS OF MOTION (ADDITIONAL)

371877 A mass \(m\) is supported by a massless string wound around a uniform hollow cylinder of mass \(m\) and radius \(R\). If the string does not slip on the cylinder, then with what acceleration will the mass release?
(Assume, \(g\) = acceleration due to gravity)

1 \(\frac{2 g}{3}\)
2 \(\frac{g}{2}\)
3 \(\frac{5 \mathrm{~g}}{6}\)
4 \(g\)
LAWS OF MOTION (ADDITIONAL)

371878 An infinite number of masses are placed on a frictionless table and they are connected via mass less strings. Their masses follow the sequence, \(m, \frac{m}{2}, \frac{m}{6}, \ldots \ldots \ldots . . . \frac{m}{n !}\), and they are further connected to a mass \(m\) that hangs over a mass less pulley. The acceleration of the hanging mass is

1 \(\frac{\mathrm{g}}{\mathrm{e}-1}\)
2 \(\frac{g}{e+1}\)
3 \(\frac{\mathrm{g}}{\mathrm{e}}\)
4 \(\frac{\mathrm{g}}{2 \mathrm{e}}\)
LAWS OF MOTION (ADDITIONAL)

371879 Three blocks of masses \(2 \mathrm{~kg} .1 \mathrm{~kg}\) and \(0.5 \mathrm{~kg}\) are connected by an inextensible string as shown below. A below of \(10 \mathrm{~N}\) is applied on the body of mass \(2 \mathrm{~kg}\). The acceleration of the system and the tensions \(T_{1}\) and \(T_{2}\) are

1 \(2.86 \mathrm{~ms}^{-2}, 4.29 \mathrm{~N}, 1.43 \mathrm{~N}\)
2 \(3.00 \mathrm{~ms}^{-2}, 5.00 \mathrm{~N}, 6.20 \mathrm{~N}\)
3 \(7.25 \mathrm{~ms}^{-2}, 2.35 \mathrm{~N}, 3.15 \mathrm{~N}\)
4 \(2.00 \mathrm{~ms}^{-2}, 4.32 \mathrm{~N}, 8.64 \mathrm{~N}\)
LAWS OF MOTION (ADDITIONAL)

371880 In the arrangement shown in the figure, work done by the string on the block of mass \(0.36 \mathrm{~kg}\) during the first second after the blocks are released from state of rest is (Ignore friction and mass of the string.)
(Acceleration due to gravity, \(\mathrm{g}=\mathbf{1 0} \mathbf{~ m s}^{-2}\) )

1 \(8 \mathrm{~J}\)
2 \(4 \mathrm{~J}\)
3 \(12 \mathrm{~J}\)
4 \(2 \mathrm{~J}\)