U Tube SHM

Q.

The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

1. 

2. 

3. 

4. 

Q. Motion of an oscillating liquid column in a U-tube is

1. periodic but not simple harmonic
2. non- periodic
3. simple harmonic and time is independent of the density of the liquid
4. simple harmonic and time period is directly proportional to the density of the liquid

Q.

Why do the deep-sea fish die when brought to the surface?

Q. The figure shows a $U-$ tube of uniform cross-sectional area $A$ having a liquid of mass $M$ and density $\rho$. If the liquid in the column is slightly displaced, then it oscillates with a time period of :
[$g=$ acceleration due to gravity]

1. $T=2\pi \sqrt{\frac{M}{g}}$
2. $T=2\pi \sqrt{\frac{MA}{g\rho }}$
3. $T=2\pi \sqrt{\frac{M}{A\rho g}}$
4. $T=2\pi \sqrt{\frac{M}{2A\rho g}}$

Q. A tray of mass M = 10 kg is supported on two identical springs, each of spring constant k. as shown in figure.When the tray is depressed a little and released, it executes simple harmonic motion of period 1.5 s. when a block of mass m is placed on the tray, the period of oscillation becomes 3.0 s.The value of m is

1. 10 kg
2. 20 kg
3. 40 kg
4. 30 kg

Q. A uniform solid cube is floating in a liquid as shown in the figure, with length $x$ inside the liquid. Some changes in parameters are mentioned in Column I. Assuming no other changes, match the following.



$\begin{array}{cc}\text{(A) If density of the liquid decreases,}x\text{will}& \text{(P) Increase}\\ \text{(B) If height of the cube is increased keeping base area and density same,}x\text{will}& \text{(Q) Decrease}\\ \text{(C) If the whole system is accelerated upward, then}x\text{will}& \text{(R) Remain same}\\ \text{(D) If the cube is replaced by another cube of same size but lesser density,}x\text{will}& \text{(S) may increase}\end{array}$

Which of the following option has the correct combination considering column-I and column-II.

1. 
   $B\to S$
2. 
   $A\to P$
3. 
   $D\to R$
4. 
   $C\to Q$

Q. A particle undergoes mutually perpendicular simple harmonic motions given by $x=a\cos \omega t$ and $y=a\sin \omega t$. The trajectory of motion of the particle will be

1. a parabola
2. a circle
3. an ellipse
4. a straight line

Q. Motion of an oscillating liquid column in a U-tube is

1. periodic but not simple harmonic
2. non- periodic
3. simple harmonic and time is independent of the density of the liquid
4. simple harmonic and time period is directly proportional to the density of the liquid

Q. What is surface energy? Establish the relation between surface tension and surface energy.

Q. Heat is being supplied at a constant rate to a sphere of ice which is melting at the rate of $0.1gm/sec$. It melts completely in $100sec$. The rate of rise of temperature thereafter will be (assume no loss of heat )

1. $0.8{}^{\circ }C/sec$
2. $3.6{}^{\circ }C/sec$
3. $5.4{}^{\circ }C/sec$
4. will change with time

Q. $T_1$, $T_2$ are time periods of oscillation of a block individually suspended to spring of force constants $K_1$ , $K_2$ respectively. If same block is suspended to parallel combination of same two springs, its time period is

1. $T_1+T_2$
2. $\frac{T_1+T_2}{2}$
3. $\frac{T_1{T}_2}{T_1+T_2}$
4. $\frac{T_1{T}_2}{\sqrt{{T_1}^2+{T_2}^2}}$

Q. A piece of gold weighs $10g$ in air and $9g$ in water. What is the volume of cavity?
(density of gold $=19.3g{cm}^{-3}$)

1. $0.182cc$
2. $0.282cc$
3. $0.382cc$
4. $0.482cc$

Q. The rectangular components of force $5dyne$ are :

1. $3$ and $4dyne$
2. $2.5$ and $25dyne$
3. $1$ and $2dyne$
4. $2$ and $3dyne$

Q. Motion of an oscillating liquid column in a U-tube is

1. periodic but not simple harmonic
2. non- periodic
3. simple harmonic and time is independent of the density of the liquid
4. simple harmonic and time period is directly proportional to the density of the liquid

Q. A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant 100 N/m. A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together. Find the amplitude of the motion?

1. $0.5m$
2. $0.05m$
3. $5m$
4. $0.02m$

Q. Try to derive the relationship between pressure and the sum of velocities (say, v) of each molecule, density of the gas ($\rho$), and the total number of particles in the container (N).

1. $\frac{1}{3}\rho \Sigma \frac{v^2}{N}$
2. $\frac{1}{2}\rho \Sigma \frac{v^2}{N}$
3. $\frac{1}{4}\rho \Sigma \frac{v^2}{N}$
4. Common man, I don't wanna do this.

Q. A particle undergoes mutually perpendicular simple harmonic motions given by $x=a\cos \omega t$ and $y=a\sin \omega t$. The trajectory of motion of the particle will be

1. an ellipse
2. a parabola
3. a circle
4. a straight line

Q. A block of weight $100N$ is lying on a rough horizontal surface.If $\mu =\frac{1}{\sqrt{3}}$ , the least possible force that can move the block is

1. $\frac{100}{\sqrt{3}}$
2. $50N$
3. $100\sqrt{3}$
4. $80\sqrt{3}$

Q. A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is $T$. If the spring is divided in two equal parts and one is used to continue the simple harmonic motion, the time period will

1. Remain $T$
2. Become $2T$
3. Become $\frac{T}{2}$
4. become $\frac{T}{\sqrt{2}}$

Q. A tray of mass M = 10 kg is supported on two identical springs, each of spring constant k. as shown in figure.When the tray is depressed a little and released, it executes simple harmonic motion of period 1.5 s. when a block of mass m is placed on the tray, the period of oscillation becomes 3.0 s.The value of m is

1. 10 kg
2. 20 kg
3. 30 kg
4. 40 kg

Q. Some liquid is filled in a cylindrical vessel of radius $R$. Let $F_1$ be the force applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square cross-section of side $R$. Let $F_2$ be the force applied by the liquid on the bottom of this new vessel. (Neglect atmosphere pressure). Then

1. $F_1=\frac{F_2}{\pi }$
2. $F_1=\sqrt{\pi F_2}$
3. $F_1=\pi F_2$
4. $F_1=F_2$

Q. Water is flowing in a river at $2m{s}^{-1}$. The river is $50m$ wide and has an average depth of $5m$. The power available from the current in the river is (Density of water $=1000kg{m}^{-3})$.

1. $0.5MW$
2. $1MW$
3. $1.5MW$
4. $2MW$

Q. The equation of a simple harmonic motion is $x=0.34\cos (3000t+0.74)$ , where $x$ and $t$ are in mm and sec respectively. The frequency of the motion is :

1. $3000$
2. $0.74/2\pi$
3. $3000/2\pi$
4. $3000/\pi$

Q. Statement 1: In simple harmonic motion, the velocity is maximum when the acceleration is minimum.
Statement 2: Displacement and velocity of $S.H.M$ differ in phase by $\frac{\pi }{2}$

1. Statement 1 is false, Statement 2 is true
2. Statement 1 is true, Statement 2 is true; Statement 2 is the correct explanation for Statement 1
3. Statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement 1
4. Statement 1 is true, Statement 2 is false

Q.

Match the statements of Column A with those of Column B.

Column A	Column B
A)sucking of a cold drink using straw	p)No liquid
B)Anaerobic bacteria	q)Cavity in a solid body
C) Archimedes principle	r) Oil lamp
D)Capillarity	s) Atmospheric pressure

1. A →q; B→ r; C → s; D → p

2. A--→s; B-r; C---→p; D---→q

3. A → r; B →s; C → p; D→ q

4. A →s; B → p; C→ q; D →r

Q. Three capillaries of same length but radii 2r, 3r, 4r are connected in series and a liquid flows through them in stream line flow. If the pressure across the third capillary is 16 mm of Hg the pressure across the first capillary will be ( in mm of Hg):

1. 25.6
2. 2.56
3. 256
4. 2560

Q. A rectangular block of mass $m$ and area of cross-section A floats in a liquid of density $\rho$. If it is given a small vertical displacement from equilibrium it undergoes with a time period $T$. Then

1. $T\propto \frac{1}{\sqrt{m}}$
2. $T\propto \sqrt{\rho }$
3. $T\propto \frac{1}{\rho }$
4. $T\propto \frac{1}{\sqrt{A}}$

Q. A particle moves in x-y plane according to the equation $\overrightarrow{r}$ = ($\hat{i}+2\hat{j}$) A cos $\omega$. The motion of the particle is:

1. on an ellipse
2. simple harmonic
3. periodic
4. on a straight line