Correlation to Linear Motion

Q. Two uniform thin rods each of length L and mass m are joined as shown in the figure.Find the dis†an ce of centre of mass of the system from point O

Q.

A grinding wheel attain a velocity of $20rad/sec$ in $5sec$ starting from rest. Find the number of revolution made by the wheel

Q. A wheel starting with angular velocity of $10\text{rad/sec}$ acquires angular velocity of $100\text{rad/sec}$ in $15\text{seconds}$. If angular acceleration of wheel is constant, what will be the angular displacement of a point on the wheel in $15\text{seconds}$?

1. $820\text{rad}$
2. $825\text{rad}$
3. $675\text{rad}$
4. $150\text{rad}$

Q.

A rigid body is one

1. the sum of distances of all particles from the axis remains constant

2. in which the distance between all pairs of particles remains fixed

3. whose centre of mass follows a parabolic path

4. whose centre of mass follows a parabolic path

Q. Select the correct option about rigid body.

1. No velocity of seperation or approach between any pair of particles.
2. No change in the distance between any pair of particles.
3. All the above are correct.
4. Shape and size of the body remains the same.

Q.

A wheel has an angular acceleration of $3.0\mathrm{rad}/{\mathrm{s}}^2$and an initial angular speed of $2.00\mathrm{rad}/\mathrm{s}$. In a time of $2\mathrm{s}$, it has rotated through an angle (in radian) of:

1. $6$

2. $12$

3. $10$

4. $4$

Q.

The ratio of the angular speeds of the hour hand and the minute hand of a clock is

1. 12:1

2. 1:6

3. 1:8

4. None of these

Q. 4.Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to theplane and passing through the point P is

Q. A fan initially rotating at $60\text{rad/sec}$ clockwise accelerates and aquires an angular velocity of $110\text{rad/sec}$ clockwise. If the angular acceleration of fan is constant and it takes $2\text{sec}$ to change its angular velocity, find the angular acceleration of the fan.

1. $50{\text{rad/sec}}^2$ in counterclockwise direction.
2. $25{\text{rad/sec}}^2$ in counterclockwise direction.
3. $25{\text{rad/sec}}^2$ in clockwise direction.
4. $50{\text{rad/sec}}^2$ in clockwise direction.

Q. For a rigid body, the angular velocity is same at ___ the points on the body.

1. All
2. Only some of
3. Never same
4. Depends of the shape of the object

Q. A uniform disc rotating with constant angular acceleration covers $50$ revolutions in the first five seconds after it starts from rest. Calculate the angular acceleration.

1. $4{\text{rev/s}}^2$
2. $2{\text{rev/s}}^2$
3. $8\pi {\text{rev/s}}^2$
4. $4\pi {\text{rev/s}}^2$

Q.

A solid body starts rotating about a stationary axis with an angular acceleration $\alpha ={\alpha }_{0}cos\phi$, $\phi$ is

the angle of rotation from the initial position. Find the angular velocity of the body as a function of the angle $\phi$.

1. 

2. 

3. 

4. 

Q.

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length $s=t^3+5$, where s is in meters and t is in seconds. The radius of the path is 20 m. The acceleration of 'P' when t = 2 s is nearly

1. 13 m/s²

2. 12 m/s²

3. 7.2 m/s²

4. 14 m/s²

Q. Find the acceleration of $\text{B}$, if the acceleration of wedge $\text{A}$ is $a$ as shown in figure.

1. $\frac{a\cos {\alpha }_2}{\cos {\alpha }_1}$
2. $\frac{\cos {\alpha }_1}{\cos {\alpha }_2}$
3. $\frac{a\cos {\alpha }_1}{\cos {\alpha }_2}$
4. $\frac{a\sin {\alpha }_1}{\cos {\alpha }_2}$

Q. 13.What is the formula of pully when given mass m1 and m2

Q.

Paragraph for below question

नीचे दिये गये प्रश्न के लिए अनुच्छेद

A uniform rod of mass ‘m’ and length ‘L’ is hung with one end hinged while other end supported with a string as shown in the figure. Answer the following questions.

‘m’ द्रव्यमान व ‘L’ लम्बाई की एक समरूप छड़ को चित्र में दर्शाए अनुसार इस प्रकार लटकाया जाता है कि इसका एक सिरा कीलकित हो जबकि दूसरा सिरा डोरी द्वारा आधारित हो। निम्नलिखित प्रश्नों के उत्तर दीजिए।

Q. The reaction force by hinge, applied on rod, just after cutting the string will be

प्रश्न - डोरी को काटने के ठीक बाद कीलक द्वारा छड़ पर आरोपित प्रतिक्रिया बल होगा

1. mg
2. $\frac{mg}{4}$
3. $\frac{mg}{2}$
4. Zero (शून्य)

Q. The angular speed (w), the radius (r), and the linear speed (v) is related as

1. v=rw
2. v=r/w
3. v=w/r
4. v=2rw

Q. The wheel of a car is rotating at the rate of 1200 revolutions per minute. On pressing the accelerator for 10 seconds, it starts rotating at 4500 revolutions per minute. The angular acceleration of the wheel is

1. $30degrees/se{c}^2$
2. $1880degrees/se{c}^2$
3. $40degrees/se{c}^2$
4. $1980degrees/se{c}^2$

Q. A wheel is performing combined translational and rotational motion on a frictionless horizontal surface on a truck which is moving with a constant linear velocity $v=10\text{m/s}$. Centre of the wheel is also moving with a constant linear velocity $v=10\text{m/s}$ with respect to ground. The wheel is rotating with angular velocity $\omega =2\text{rad/s}$. Find velocity of point $A$ (Which is the topmost point of wheel as shown in the figure) with respect to ground. Radius of the wheel is $1\text{m}$.

1. $10\hat{i}$
2. $8\hat{i}$
3. $6\hat{i}$
4. zero

Q. A fan initially rotating at $60\text{rad/sec}$ clockwise accelerates and aquires an angular velocity of $110\text{rad/sec}$ clockwise. If the angular acceleration of fan is constant and it takes $2\text{sec}$ to change its angular velocity, find the angular acceleration of the fan.

1. $50{\text{rad/sec}}^2$ in counterclockwise direction.
2. $25{\text{rad/sec}}^2$ in counterclockwise direction.
3. $25{\text{rad/sec}}^2$ in clockwise direction.
4. $50{\text{rad/sec}}^2$ in clockwise direction.

Q. The angular speed (w), the radius (r), and the linear speed (v) is related as

1. v=rw
2. v=r/w
3. v=w/r
4. v=2rw

Q. Paragraph for below question

नीचे दिए गए प्रश्न के लिए अनुच्छेद

A uniform rod of mass M and length l = 1 m hinged at A in the vertical plane, is released from rest when it is in horizontal position. At angular position θ = 60°, angular velocity of rod is ω. Then [g = 10 m/s²]

जब ऊर्ध्वाधर तल में A पर किलकित द्रव्यमान M व लम्बाई l = 1 m की एक समरूप छड़ क्षैतिज स्थिति में है, तब इसे विराम से छोड़ा जाता है। कोणीय स्थिति θ = 60° पर, छड़ का कोणीय वेग ω है। तब [g = 10 m/s²]


Q. Tangential acceleration of end B at angular position, θ = 60° is

प्रश्न - कोणीय स्थिति θ = 60° पर, सिरे B का स्पर्शरेखीय त्वरण है

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

Q. Angular speed of particle undergoing circular motion of radius $2\text{m}$ varies with time(s) as $\omega =(2t+1)$ rad/s. Distance travelled by particle in $0$ to $1\text{s}$ is

1. $3\text{m}$
2. $1\text{m}$
3. $4\text{m}$
4. $2\text{m}$

Q. A wheel completes 2000 rotations in covering a distance of 9.5 km. The diameter of the wheel is

1. 1.5 m
2. 1.5 cm
3. 7.5 m
4. 7.5 cm

Q. Find the incorrect option for the general rotation of a wheel of radius $r$ which can be viewed as pure translation with velocity $\overrightarrow{V_0}$ and pure rotation about $\text{O}$ with $\overrightarrow{\omega }$.

1. $\overrightarrow{V_A}=\overrightarrow{V_0}+\overrightarrow{\omega }\times {\overrightarrow{r}}_{AO}$
2. $\overrightarrow{V_B}=\overrightarrow{V_0}+\overrightarrow{\omega }\times {\overrightarrow{r}}_{CO}$
3. ${\overrightarrow{V}}_{AO}=\overrightarrow{\omega }\times {\overrightarrow{r}}_{AO}$
4. ${\overrightarrow{V}}_{AO}=\overrightarrow{V_0}+\overrightarrow{\omega }\times {\overrightarrow{r}}_{AO}$

Q. When a person throws a meter stick, it is found that the centre of the stick is moving with a speed of $10\text{m/s}$ vertically upward & the left end of the stick with a speed $20\text{m/s}$ vertically upward. Then, the angular speed of the stick is

1. $20\text{rad/sec}$
2. $10\text{rad/sec}$
3. $30\text{rad/sec}$
4. None of the these

Q. Paragraph for below question

नीचे दिए गए प्रश्न के लिए अनुच्छेद

A uniform rod of mass M and length l = 1 m hinged at A in the vertical plane, is released from rest when it is in horizontal position. At angular position θ = 60°, angular velocity of rod is ω. Then [g = 10 m/s²]

जब ऊर्ध्वाधर तल में A पर किलकित द्रव्यमान M व लम्बाई l = 1 m की एक समरूप छड़ क्षैतिज स्थिति में है, तब इसे विराम से छोड़ा जाता है। कोणीय स्थिति θ = 60° पर, छड़ का कोणीय वेग ω है। तब [g = 10 m/s²]


Q. Angular velocity (ω) of the rod is

प्रश्न - छड़ का कोणीय वेग (ω) है

1. $\sqrt{30}\text{rad/s}$
   
2. $\sqrt{15}\text{rad/s}$
   
3. $\sqrt{10}\text{rad/s}$
   
4. $\sqrt{5}\text{rad/s}$
   

Q. A disc having radius $r=1\text{m}$ and $m=2\text{kg}$ is rotating about an axis passing through its COM and perpendicular to the plane of disc. Initial velocity of a point $A$ at the edge of disc is $6\text{m/s}$. A retarding torque of magnitude $2\text{Nm}$ starts acting on disc about its axis of rotation. Find the velocity of point $A$ after $t=2\text{s}$.

1. $1\text{m/s}$
2. $3\text{m/s}$
3. $4\text{m/s}$
4. $2\text{m/s}$

Q. The speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks:

Q. As a part of a maintenance inspection the compressor of a jet engine is made to spin according to the graph as shown. The number of revolutions made by the compressor during the test is

1. 9000
2. 16570
3. 12750
4. 11250