Physical Pendulum

Q.

Moment of inertia of a solid sphere of mass M and radius R is ______.

Q.

Derive an expression for the gravitational field due to a uniform rod of length L and mass M at a point on its perpendicular bisector at a distance d from the centre.

Q.

A simple pendulum is made of a bob which is a hollow sphere containing mercury, suspended by a means of a wire. If mercury is drained off continuously the period of the pendulum will

A) remain unchanged.

B) first increase, then decrease

C) decreases.

D) become erratic

and Why?

Q. A metre stick swinging in a vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillations of frequency $f_0$. If the bottom half of the stick is cut off and glued to the upper half, then the new frequency for small oscillations is

1. $f=\sqrt{2}{f}_0$
2. $f=\frac{1}{\sqrt{2}}{f}_0$
3. $f=\sqrt{3}{f}_0$
4. $f=f_0$

Q.

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits -∅and +∅. For an angular displacement $\theta (|\theta |<\varphi )$ , the tension in the string and the velocity of the bob are T and v respectively. The following relations hold good under the above conditions

1. 

2. 

3. 

4. 

Q.

If $a$ vector of magnitude $50$ is collinear with the vector$b=6i-8j-15/2k$ and makes an acute angle with the positive direction of the Z-axis, then the vector $a$ is equal to?

1. $a=4b$

2. $a=-4b$

3. $b=4a$

4. None of these

Q.

The period of a simple pendulum is doubled, when

1. Its length is doubled

2. The mass of the bob is doubled

3. Its length is made four times

4. The mass of the bob and the length of the pendulum are doubled

Q. What is the period of a pendulum formed by pivoting a meter stick so that it is free to rotate about a horizontal axis passing through the $75\text{cm}$ mark?

1. $1.00\text{sec}$
2. $1.53\text{sec}$
3. $1.25\text{sec}$
4. $2.5\text{sec}$

Q.

If the length of the simple pendulum increases, its time period decreases.

1. True
2. False

Q.

The length of a second pendulum is 100 cm whose time period is 1.4 sec.

Q. In simple pendulum at lowest point tangential acceleration is zero. Why?

Q. Pendulum $A$ is a physical pendulum made from a thin, rigid, uniform rod whose length is $d$. One end of this rod is attached to the ceiling by a frictionless hinge so that the rod is free to swing back and forth. Pendulum $B$ is a simple pendulum whose length is also $d$. If the ratio of time periods of their small angle oscillations is found to be $\frac{T_A}{T_B}=\sqrt{\frac{x}{3}},$ the value of $x$ is

Q. In the given figure an L-shaped bar of mass $M$ is pivoted at one of its end, so that it can freely rotate in a vertical plane. Find the frequency of oscillation, if it is slightly disturbed from its equilibrium position.

1. $\frac{1}{2\pi }\sqrt{\frac{g}{L}}$
2. $\frac{1}{2\pi }\sqrt{\frac{3g\sqrt{10}}{4L}}$
3. $\frac{1}{2\pi }\sqrt{\frac{3g}{4L}}$
4. $\frac{1}{2\pi }\sqrt{\frac{3g\sqrt{5}}{4L}}$

Q. A ball at O is in equilibrium as it is attached with two strings AO and DO which are tied at A and D. $AO=DO=a\sqrt{5}$.

The charges at A, B, C and D are +q, +Q, +2Q and -q respectively. The ball O is positively charged then

1. The ball O can not remain in equilibrium.
2. If the charge at C is +Q, the ball will remain in equilibrium.
3. The ball at O will remain in equilibrium.
4. If the charges at A and D and charges at B and C are interchanged, the ball will remain in equilibrium.

Q. A student measuring the diameter of a pencil of circular cross - section with the help of a vernier scale records the following four readings $5.50\text{mm},$ $5.55\text{mm,}$$5.45\text{mm},5.65\text{mm}.$ The average of these four reading is $5.5375\text{mm}$ and the standard deviation of the data is $0.07395\text{mm}.$ The average diameter of the pencil should therefore be recorded as :

1. $(5.5375\pm 0.0739)\text{mm}$
2. $(5.5375\pm 0.0740)\text{mm}$
3. $(5.538\pm 0.074)\text{mm}$
4. $(5.54\pm 0.07)\text{mm}$

Q.

A uniform square lamina of side 2a is hung up by one corner and oscillates in its own plane which is vertical. Find the length of the equivalent simple pendulum.

1. 

2. 

3. 

4. 

Q.

Two bodies are projected at angles θ and (90⁰−θ) to the horizontal with the same speed. The ratio of their times of flight is

1. $\sin \theta :1$

2. $\cos \theta :1$

3. $\sin \theta :\cos \theta$

4. $\cos \theta :\sin \theta$

Q.

If $\frac{x^2}{36}-\frac{y^2}{k^2}=1$ is a hyperbola, then which of the following statements can be correct?

1. $(-3,1)$ lies on the hyperbola

2. $(3,1)$ lies on the hyperbola

3. $(10,4)$ lies on the hyperbola

4. $(5,2)$ lies on the hyperbola

Q. A pendulum oscillates 60 times in 5 seconds . Find time period and frequency.

Q. Time is measured using periodic motion described as

Q.

Does the time period of a pendulum depend on the length of a pendulum ?

Q.

In $∆ABC$ with usual notation, observe the two statements given below

$$\begin{gathered} \text{I}.r{r}_1{r}_2{r}_3={∆}^2 \\ \text{II}.r_1{r}_2+r_2{r}_3+r_3{r}_1=s^2 \end{gathered}$$

Which of the following is correct?

1. Both $\text{I}$ and $\text{II}$ are correct

2. $\text{I}$ and $\text{II}$ are incorrect

3. $\text{I}$ is incorrect, $\text{II}$ is correct

4. $\text{I}$ is correct, $\text{II}$ is incorrect

Q. The period of oscillation of a simple pendulum is given by the relation T = 2 pie root under L/g. The measured value of length London and the period of oscillations for 50 oscillations are (20.0 +- 0.1)cm and (45+-1) sec respectively. Find the absolute error in determination of g.

Q.

Find the time period of small oscillations of the following systems.

(p) A metre stick suspended through the 20 cm mark.

(q) A ring of mass m and radius r suspended through a point on its periphery.

(r) A uniform square plate of edge 'a' suspended through a corner.

(s) A uniform disc of mass m and radius r suspended through a point $\frac{r}{2}$ away from the centre.

(i)$2\pi \sqrt{\frac{2\sqrt{2}a}{3g}}$ (ii) 1.51 sec (iii) $2\pi \sqrt{\frac{3r}{3g}}$ (iv)$T=2\pi \sqrt{\frac{2R}{g}}$

1. p - (i) ; q - (iii) ; r - (ii) ; s-(iv)

2. p - (ii) ; q - (i) ; r - (iii) ; s-(iv)

3. p - (iv) ; q - (iii) ; r - (ii) ; s-(i)

4. p - (ii) ; q - (iv) ; r - (i) ; s-(iii)

Q.

A disc is suspended at a point $\frac{R}{2}$ above its center, Find its period of oscillation.

1. 

2. 

3. 

4. 

Q. The time period of oscillations of a simple pendulum is $1$ minute. If its length is increased by $44\%$ then its new time period of oscillation will be

1. $96s$
2. $58s$
3. $12s$
4. $72s$

Q.

A uniform disc of radius r is to be suspended through a small hole made in the disc. Find the minimum possible time period of the disc for small oscillations. What should be the distance of the hole from the centre for it to have minimum time period?

1. 

2. 

3. 

4. 

Q.

A physical pendulum consists of three equal thin bars of length l and mass m which forms an equilateral triangle as shown in figure.Find the angular frequency of small oscillations.

1. 

2. 

3. 

4. 

Q. How does the time period of a simple pendulum depend on the :
(i) length of pendulum
(ii) mass of bob?

Q.

The time period of a pendulum depends upon its

1. Mass of bob

2. Length of string

3. Dimension of bob

4. Material of the bob