363294
An aircraft is moving with uniform velocity \(150\,m/s\) in space. If all the forces acting on it are balanced, then it will
1 Keep moving with same velocity
2 Remain floating at its place
3 Escape in space
4 Fall down on earth
Explanation:
As all the forces acting on the aircraft are balanced, the net force on it will be zero. Thus, the aircraft will keep moving with the same velocity of \(150\,m/s\).
MHTCET - 2019
PHXI05:LAWS OF MOTION
363295
If the shown system is in equilibrium, then which of the following options is correct?
1 \({T_{1}=T_{2} \neq T_{3}}\)
2 \({T_{1} \neq T_{2}=T_{3}}\)
3 \({T_{1}=T_{2}=T_{3}}\)
4 \({T_{1} \neq T_{2} \neq T_{3}}\)
Explanation:
The resolution of tensions are shown in the following figure. \({T_{3}=W_{2} \quad}\) and \({\quad T_{3}=T_{2}}\) (same rope) \({T_{1} \sin \theta=T_{2} \sin \theta \Rightarrow T_{1}=T_{2}}\) Hence, \({T_{1}=T_{2}=T_{3}}\)
PHXI05:LAWS OF MOTION
363296
A mass \(M\) is hung with light inextensible strings as shown in the figure. The tension in the horizontal string is
1 \(\sqrt 3 \,Mg\)
2 \(\sqrt 2 \,Mg\)
3 \(\dfrac{M g}{\sqrt{3}}\)
4 \(\dfrac{M g}{2}\)
Explanation:
According to Lami's theorem, \(\frac{{{T_1}}}{{\sin \,120^\circ }} = \frac{{{T_2}}}{{\sin \,90^\circ }} = \frac{{Mg}}{{\sin \,150^\circ }}\) \(\frac{{2{T_1}}}{{\sqrt 3 }} = \frac{{{T_2}}}{1} = 2Mg\) or \({T_1} = \sqrt 3 \,Mg\)
PHXI05:LAWS OF MOTION
363297
A string of negligible mass going over a clamped pulley of mass \(m\) supports a block of mass \(M\) as shown in the figure. The force on the pulley by the clamp is given by
1 \(\sqrt 2 \,Mg\)
2 \(\sqrt 2 \,mg\)
3 \(g\sqrt {{{(M + m)}^2} + {m^2}} \)
4 \(g\sqrt {{{(M + m)}^2} + {M^2}} \)
Explanation:
Force on the pulley by the clamp \(F = \sqrt {{T^2} + {{[(M + m)g]}^2}} \) \(F = \sqrt {{{(Mg)}^2} + {{[(M + m)g]}^2}} \) \(F = g\sqrt {{M^2} + {{(M + m)}^2}} \)
363294
An aircraft is moving with uniform velocity \(150\,m/s\) in space. If all the forces acting on it are balanced, then it will
1 Keep moving with same velocity
2 Remain floating at its place
3 Escape in space
4 Fall down on earth
Explanation:
As all the forces acting on the aircraft are balanced, the net force on it will be zero. Thus, the aircraft will keep moving with the same velocity of \(150\,m/s\).
MHTCET - 2019
PHXI05:LAWS OF MOTION
363295
If the shown system is in equilibrium, then which of the following options is correct?
1 \({T_{1}=T_{2} \neq T_{3}}\)
2 \({T_{1} \neq T_{2}=T_{3}}\)
3 \({T_{1}=T_{2}=T_{3}}\)
4 \({T_{1} \neq T_{2} \neq T_{3}}\)
Explanation:
The resolution of tensions are shown in the following figure. \({T_{3}=W_{2} \quad}\) and \({\quad T_{3}=T_{2}}\) (same rope) \({T_{1} \sin \theta=T_{2} \sin \theta \Rightarrow T_{1}=T_{2}}\) Hence, \({T_{1}=T_{2}=T_{3}}\)
PHXI05:LAWS OF MOTION
363296
A mass \(M\) is hung with light inextensible strings as shown in the figure. The tension in the horizontal string is
1 \(\sqrt 3 \,Mg\)
2 \(\sqrt 2 \,Mg\)
3 \(\dfrac{M g}{\sqrt{3}}\)
4 \(\dfrac{M g}{2}\)
Explanation:
According to Lami's theorem, \(\frac{{{T_1}}}{{\sin \,120^\circ }} = \frac{{{T_2}}}{{\sin \,90^\circ }} = \frac{{Mg}}{{\sin \,150^\circ }}\) \(\frac{{2{T_1}}}{{\sqrt 3 }} = \frac{{{T_2}}}{1} = 2Mg\) or \({T_1} = \sqrt 3 \,Mg\)
PHXI05:LAWS OF MOTION
363297
A string of negligible mass going over a clamped pulley of mass \(m\) supports a block of mass \(M\) as shown in the figure. The force on the pulley by the clamp is given by
1 \(\sqrt 2 \,Mg\)
2 \(\sqrt 2 \,mg\)
3 \(g\sqrt {{{(M + m)}^2} + {m^2}} \)
4 \(g\sqrt {{{(M + m)}^2} + {M^2}} \)
Explanation:
Force on the pulley by the clamp \(F = \sqrt {{T^2} + {{[(M + m)g]}^2}} \) \(F = \sqrt {{{(Mg)}^2} + {{[(M + m)g]}^2}} \) \(F = g\sqrt {{M^2} + {{(M + m)}^2}} \)
363294
An aircraft is moving with uniform velocity \(150\,m/s\) in space. If all the forces acting on it are balanced, then it will
1 Keep moving with same velocity
2 Remain floating at its place
3 Escape in space
4 Fall down on earth
Explanation:
As all the forces acting on the aircraft are balanced, the net force on it will be zero. Thus, the aircraft will keep moving with the same velocity of \(150\,m/s\).
MHTCET - 2019
PHXI05:LAWS OF MOTION
363295
If the shown system is in equilibrium, then which of the following options is correct?
1 \({T_{1}=T_{2} \neq T_{3}}\)
2 \({T_{1} \neq T_{2}=T_{3}}\)
3 \({T_{1}=T_{2}=T_{3}}\)
4 \({T_{1} \neq T_{2} \neq T_{3}}\)
Explanation:
The resolution of tensions are shown in the following figure. \({T_{3}=W_{2} \quad}\) and \({\quad T_{3}=T_{2}}\) (same rope) \({T_{1} \sin \theta=T_{2} \sin \theta \Rightarrow T_{1}=T_{2}}\) Hence, \({T_{1}=T_{2}=T_{3}}\)
PHXI05:LAWS OF MOTION
363296
A mass \(M\) is hung with light inextensible strings as shown in the figure. The tension in the horizontal string is
1 \(\sqrt 3 \,Mg\)
2 \(\sqrt 2 \,Mg\)
3 \(\dfrac{M g}{\sqrt{3}}\)
4 \(\dfrac{M g}{2}\)
Explanation:
According to Lami's theorem, \(\frac{{{T_1}}}{{\sin \,120^\circ }} = \frac{{{T_2}}}{{\sin \,90^\circ }} = \frac{{Mg}}{{\sin \,150^\circ }}\) \(\frac{{2{T_1}}}{{\sqrt 3 }} = \frac{{{T_2}}}{1} = 2Mg\) or \({T_1} = \sqrt 3 \,Mg\)
PHXI05:LAWS OF MOTION
363297
A string of negligible mass going over a clamped pulley of mass \(m\) supports a block of mass \(M\) as shown in the figure. The force on the pulley by the clamp is given by
1 \(\sqrt 2 \,Mg\)
2 \(\sqrt 2 \,mg\)
3 \(g\sqrt {{{(M + m)}^2} + {m^2}} \)
4 \(g\sqrt {{{(M + m)}^2} + {M^2}} \)
Explanation:
Force on the pulley by the clamp \(F = \sqrt {{T^2} + {{[(M + m)g]}^2}} \) \(F = \sqrt {{{(Mg)}^2} + {{[(M + m)g]}^2}} \) \(F = g\sqrt {{M^2} + {{(M + m)}^2}} \)
363294
An aircraft is moving with uniform velocity \(150\,m/s\) in space. If all the forces acting on it are balanced, then it will
1 Keep moving with same velocity
2 Remain floating at its place
3 Escape in space
4 Fall down on earth
Explanation:
As all the forces acting on the aircraft are balanced, the net force on it will be zero. Thus, the aircraft will keep moving with the same velocity of \(150\,m/s\).
MHTCET - 2019
PHXI05:LAWS OF MOTION
363295
If the shown system is in equilibrium, then which of the following options is correct?
1 \({T_{1}=T_{2} \neq T_{3}}\)
2 \({T_{1} \neq T_{2}=T_{3}}\)
3 \({T_{1}=T_{2}=T_{3}}\)
4 \({T_{1} \neq T_{2} \neq T_{3}}\)
Explanation:
The resolution of tensions are shown in the following figure. \({T_{3}=W_{2} \quad}\) and \({\quad T_{3}=T_{2}}\) (same rope) \({T_{1} \sin \theta=T_{2} \sin \theta \Rightarrow T_{1}=T_{2}}\) Hence, \({T_{1}=T_{2}=T_{3}}\)
PHXI05:LAWS OF MOTION
363296
A mass \(M\) is hung with light inextensible strings as shown in the figure. The tension in the horizontal string is
1 \(\sqrt 3 \,Mg\)
2 \(\sqrt 2 \,Mg\)
3 \(\dfrac{M g}{\sqrt{3}}\)
4 \(\dfrac{M g}{2}\)
Explanation:
According to Lami's theorem, \(\frac{{{T_1}}}{{\sin \,120^\circ }} = \frac{{{T_2}}}{{\sin \,90^\circ }} = \frac{{Mg}}{{\sin \,150^\circ }}\) \(\frac{{2{T_1}}}{{\sqrt 3 }} = \frac{{{T_2}}}{1} = 2Mg\) or \({T_1} = \sqrt 3 \,Mg\)
PHXI05:LAWS OF MOTION
363297
A string of negligible mass going over a clamped pulley of mass \(m\) supports a block of mass \(M\) as shown in the figure. The force on the pulley by the clamp is given by
1 \(\sqrt 2 \,Mg\)
2 \(\sqrt 2 \,mg\)
3 \(g\sqrt {{{(M + m)}^2} + {m^2}} \)
4 \(g\sqrt {{{(M + m)}^2} + {M^2}} \)
Explanation:
Force on the pulley by the clamp \(F = \sqrt {{T^2} + {{[(M + m)g]}^2}} \) \(F = \sqrt {{{(Mg)}^2} + {{[(M + m)g]}^2}} \) \(F = g\sqrt {{M^2} + {{(M + m)}^2}} \)
