Some Systems Executing Simple Harmonic Motion
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI14:OSCILLATIONS

364334 A bead of mass \(m\) can slide on a frictionless wire as shown in figure. Because of the given shape of the wire near \(P\), the bottom point, it can be approximated as a parabola. Near \(P\), the potential energy of the bead is given \(U=c x^{2}\) where \(c\) is a constant and \(x\) is measured from \(P\). The bead, if displaced slightly from point \(P\) will oscillate about \(P\). The period of oscillation is
supporting img

1 \(2 \pi \sqrt{m / c}\)
2 \(2 \pi \sqrt{m / 2 c}\)
3 \(2 \pi \sqrt{c / m}\)
4 \(2 \pi \sqrt{2 c / m}\)
PHXI14:OSCILLATIONS

364335 A cylindrical block of wood (density \( = 650\;kg\;{m^{ - 3}}\)), of base area \(30\;c{m^2}\) and height \(54\;cm\), floats in a liquid of density \(900\;kg\;{m^{ - 3}}\). The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly):

1 \(52\;cm\)
2 \(65\;cm\)
3 \(39\;cm\)
4 \(29\;cm\)
PHXI14:OSCILLATIONS

364336 A tunnel is made across the earth of radius \(R\), passing through its centre. A ball is dropped from a height h in the tunnel. the motion will be periodic with time period.

1 \(2 \pi \sqrt{\dfrac{R}{g}}+4 \sqrt{\dfrac{2 h}{g}}\)
2 \(2 \pi \sqrt{\dfrac{R}{g}}+4 \sqrt{\dfrac{h}{g}}\)
3 \(2 \pi \sqrt{\dfrac{R}{g}}+\sqrt{\dfrac{h}{g}}\)
4 \(2 \pi \sqrt{\dfrac{R}{g}}+\sqrt{\dfrac{2 h}{g}}\)
PHXI14:OSCILLATIONS

364337 A wire is bent at an angle \(\theta\). A rod of mass \(m\) can slide along the bent wire without friction as shown in Fig. Soap film is maintained in the frame kept in a vertical position and the rod is in equilibrium as shown in the figure. If rod is displaced slightly in vertical direction, then the time period of small oscillation of the rod is
supporting img

1 \(2 \pi \sqrt{\dfrac{l}{g}}\)
2 \(2 \pi \sqrt{\dfrac{l \cos \theta}{g}}\)
3 \(2 \pi \sqrt{\dfrac{l}{g \cos \theta}}\)
4 \(2 \pi \sqrt{\dfrac{l}{g \tan \theta}}\)
PHXI14:OSCILLATIONS

364334 A bead of mass \(m\) can slide on a frictionless wire as shown in figure. Because of the given shape of the wire near \(P\), the bottom point, it can be approximated as a parabola. Near \(P\), the potential energy of the bead is given \(U=c x^{2}\) where \(c\) is a constant and \(x\) is measured from \(P\). The bead, if displaced slightly from point \(P\) will oscillate about \(P\). The period of oscillation is
supporting img

1 \(2 \pi \sqrt{m / c}\)
2 \(2 \pi \sqrt{m / 2 c}\)
3 \(2 \pi \sqrt{c / m}\)
4 \(2 \pi \sqrt{2 c / m}\)
PHXI14:OSCILLATIONS

364335 A cylindrical block of wood (density \( = 650\;kg\;{m^{ - 3}}\)), of base area \(30\;c{m^2}\) and height \(54\;cm\), floats in a liquid of density \(900\;kg\;{m^{ - 3}}\). The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly):

1 \(52\;cm\)
2 \(65\;cm\)
3 \(39\;cm\)
4 \(29\;cm\)
PHXI14:OSCILLATIONS

364336 A tunnel is made across the earth of radius \(R\), passing through its centre. A ball is dropped from a height h in the tunnel. the motion will be periodic with time period.

1 \(2 \pi \sqrt{\dfrac{R}{g}}+4 \sqrt{\dfrac{2 h}{g}}\)
2 \(2 \pi \sqrt{\dfrac{R}{g}}+4 \sqrt{\dfrac{h}{g}}\)
3 \(2 \pi \sqrt{\dfrac{R}{g}}+\sqrt{\dfrac{h}{g}}\)
4 \(2 \pi \sqrt{\dfrac{R}{g}}+\sqrt{\dfrac{2 h}{g}}\)
PHXI14:OSCILLATIONS

364337 A wire is bent at an angle \(\theta\). A rod of mass \(m\) can slide along the bent wire without friction as shown in Fig. Soap film is maintained in the frame kept in a vertical position and the rod is in equilibrium as shown in the figure. If rod is displaced slightly in vertical direction, then the time period of small oscillation of the rod is
supporting img

1 \(2 \pi \sqrt{\dfrac{l}{g}}\)
2 \(2 \pi \sqrt{\dfrac{l \cos \theta}{g}}\)
3 \(2 \pi \sqrt{\dfrac{l}{g \cos \theta}}\)
4 \(2 \pi \sqrt{\dfrac{l}{g \tan \theta}}\)
PHXI14:OSCILLATIONS

364334 A bead of mass \(m\) can slide on a frictionless wire as shown in figure. Because of the given shape of the wire near \(P\), the bottom point, it can be approximated as a parabola. Near \(P\), the potential energy of the bead is given \(U=c x^{2}\) where \(c\) is a constant and \(x\) is measured from \(P\). The bead, if displaced slightly from point \(P\) will oscillate about \(P\). The period of oscillation is
supporting img

1 \(2 \pi \sqrt{m / c}\)
2 \(2 \pi \sqrt{m / 2 c}\)
3 \(2 \pi \sqrt{c / m}\)
4 \(2 \pi \sqrt{2 c / m}\)
PHXI14:OSCILLATIONS

364335 A cylindrical block of wood (density \( = 650\;kg\;{m^{ - 3}}\)), of base area \(30\;c{m^2}\) and height \(54\;cm\), floats in a liquid of density \(900\;kg\;{m^{ - 3}}\). The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly):

1 \(52\;cm\)
2 \(65\;cm\)
3 \(39\;cm\)
4 \(29\;cm\)
PHXI14:OSCILLATIONS

364336 A tunnel is made across the earth of radius \(R\), passing through its centre. A ball is dropped from a height h in the tunnel. the motion will be periodic with time period.

1 \(2 \pi \sqrt{\dfrac{R}{g}}+4 \sqrt{\dfrac{2 h}{g}}\)
2 \(2 \pi \sqrt{\dfrac{R}{g}}+4 \sqrt{\dfrac{h}{g}}\)
3 \(2 \pi \sqrt{\dfrac{R}{g}}+\sqrt{\dfrac{h}{g}}\)
4 \(2 \pi \sqrt{\dfrac{R}{g}}+\sqrt{\dfrac{2 h}{g}}\)
PHXI14:OSCILLATIONS

364337 A wire is bent at an angle \(\theta\). A rod of mass \(m\) can slide along the bent wire without friction as shown in Fig. Soap film is maintained in the frame kept in a vertical position and the rod is in equilibrium as shown in the figure. If rod is displaced slightly in vertical direction, then the time period of small oscillation of the rod is
supporting img

1 \(2 \pi \sqrt{\dfrac{l}{g}}\)
2 \(2 \pi \sqrt{\dfrac{l \cos \theta}{g}}\)
3 \(2 \pi \sqrt{\dfrac{l}{g \cos \theta}}\)
4 \(2 \pi \sqrt{\dfrac{l}{g \tan \theta}}\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI14:OSCILLATIONS

364334 A bead of mass \(m\) can slide on a frictionless wire as shown in figure. Because of the given shape of the wire near \(P\), the bottom point, it can be approximated as a parabola. Near \(P\), the potential energy of the bead is given \(U=c x^{2}\) where \(c\) is a constant and \(x\) is measured from \(P\). The bead, if displaced slightly from point \(P\) will oscillate about \(P\). The period of oscillation is
supporting img

1 \(2 \pi \sqrt{m / c}\)
2 \(2 \pi \sqrt{m / 2 c}\)
3 \(2 \pi \sqrt{c / m}\)
4 \(2 \pi \sqrt{2 c / m}\)
PHXI14:OSCILLATIONS

364335 A cylindrical block of wood (density \( = 650\;kg\;{m^{ - 3}}\)), of base area \(30\;c{m^2}\) and height \(54\;cm\), floats in a liquid of density \(900\;kg\;{m^{ - 3}}\). The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly):

1 \(52\;cm\)
2 \(65\;cm\)
3 \(39\;cm\)
4 \(29\;cm\)
PHXI14:OSCILLATIONS

364336 A tunnel is made across the earth of radius \(R\), passing through its centre. A ball is dropped from a height h in the tunnel. the motion will be periodic with time period.

1 \(2 \pi \sqrt{\dfrac{R}{g}}+4 \sqrt{\dfrac{2 h}{g}}\)
2 \(2 \pi \sqrt{\dfrac{R}{g}}+4 \sqrt{\dfrac{h}{g}}\)
3 \(2 \pi \sqrt{\dfrac{R}{g}}+\sqrt{\dfrac{h}{g}}\)
4 \(2 \pi \sqrt{\dfrac{R}{g}}+\sqrt{\dfrac{2 h}{g}}\)
PHXI14:OSCILLATIONS

364337 A wire is bent at an angle \(\theta\). A rod of mass \(m\) can slide along the bent wire without friction as shown in Fig. Soap film is maintained in the frame kept in a vertical position and the rod is in equilibrium as shown in the figure. If rod is displaced slightly in vertical direction, then the time period of small oscillation of the rod is
supporting img

1 \(2 \pi \sqrt{\dfrac{l}{g}}\)
2 \(2 \pi \sqrt{\dfrac{l \cos \theta}{g}}\)
3 \(2 \pi \sqrt{\dfrac{l}{g \cos \theta}}\)
4 \(2 \pi \sqrt{\dfrac{l}{g \tan \theta}}\)