1
MHT CET 2023 14th May Evening Shift
+1
-0

A uniform circular disc of mass $$12 \mathrm{~kg}$$ is held by two identical springs. When the disc is slightly pressed down and released, it executes S.H.M. of period 2 second. The force constant of each spring is (nearly) (Take $$\pi^2=10$$ )

A
230 Nm$$^{-1}$$
B
120 Nm$$^{-1}$$
C
60 Nm$$^{-1}$$
D
30 Nm$$^{-1}$$
2
MHT CET 2023 14th May Evening Shift
+1
-0

A light spring is suspended with mass $$m_1$$ at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is $$T$$ second. When a mass $$m_2$$ is added to $$m_1$$ and the system is made to oscillate, the period is found to be $$\frac{3}{2} T$$. The ratio $$m_1: m_2$$ is

A
$$2: 3$$
B
$$3: 4$$
C
$$4: 5$$
D
$$5: 6$$
3
MHT CET 2023 14th May Evening Shift
+1
-0

A block of mass '$$M$$' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that the mass is separated from the piston, is (acceleration due to gravity, $$\mathrm{g}=10 \mathrm{~ms}^{-2}, \pi^2=10$$ )

A
0.25 m
B
0.5 m
C
1 m
D
$$\infty$$
4
MHT CET 2023 14th May Morning Shift
+1
-0

A simple pendulum of length '$$l$$' and a bob of mass '$$\mathrm{m}$$' is executing S.H.M. of small amplitude '$$A$$'. The maximum tension in the string will be ($$\mathrm{g}=$$ acceleration due to gravity)

A
$$2 \mathrm{~mg}$$
B
$$\mathrm{mg}\left[1+\left(\frac{\mathrm{A}}{\ell}\right)^2\right]$$
C
$$\mathrm{mg}\left[1+\left(\frac{\mathrm{A}}{\ell}\right)\right]^2$$
D
$$m g\left[1+\left(\frac{\mathrm{A}}{\ell}\right)\right]$$
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