# Physics

### Practice Papers

- Physics & Chemistry

http://www.deeper.co.in/files/TrialSet/PC.pdf

- Solution ( Physics Chemistry Mathematics Biology )

http://www.deeper.co.in/files/TrialSet/Web-Paper-2011-Answer-Keys.pdf

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### Practice Papers

- Physics & Chemistry

http://www.deeper.co.in/files/TrialSet/PC.pdf

- Solution ( Physics Chemistry Mathematics Biology )

http://www.deeper.co.in/files/TrialSet/Web-Paper-2011-Answer-Keys.pdf

### Circular Motion

**Important Information**

**When a body moves along a circular path with uniform speed, it is said to perform a uniform circular motion (U.C.M.).**

**In U.C.M.**

**1. Angular speed of a particle,**

**Where θ is the angular displacement in time‘t’. T is the period of revolution of the particle performing a U.C.M. and n is the frequency of revolution i.e. no .of revolutions completed by the particle per second. S.I. unit of ω is rad/s.**

**Angular Velocity (ω): It is the rate of change of angular displacement w.r.t. time.**

**2. The linear speed of a particle v = rω where r is the radius of the circle.**

**3. S.I. unit of α is rad/sec**

^{2}**Linear acceleration (a) = r α.**

**4. In U.C.M. the acceleration is always directed along the radius, towards the centre of the circle. It is called radial or centripetal acceleration. The magnitude of C.P. acceleration is . If m is the mass of the body performing U.C.M., then the centripetal force acting upon it is . It is also given by**

**The radial acceleration**

**5. If the angular acceleration α is constant then for accelerated circular motion,**

**(i)**

**(ii)**

**(iii)**

**Where ω**

_{0}is the angular speed of the particle at time t = 0 and ω is the angular speed of the particle after time‘t’.**6. Banking of Roads: For a vehicle moving along a circular track of radius r, banked at an angle θ, the maximum speed limit for the safety of the vehicle is given by**

**V is also known as critical speed. In the case of a train, the elevation of the outer rail above the inner rail is given by**

**h = ℓ sin θ.**

**Where is the distance between the rails.**

**For a metre gauge railway,**

**7. For a vehicle moving along a horizontal curve of radius r, (unbanked circular road), the C.P. force is provided by the friction. The maximum safe speed (v) is calculated by using the relation**

**Where μ is the coefficient of friction between the tyres of the car and the surface of the road.**

**8. A cyclist, moving with a speed v, along a horizontal curved road of radius r, has to lean inwards to keep his balance. His angle of inclination (θ) with the vertical is given by**

**9.**

**10.**

**11. Direction of are given by right hand thumb rule.**

**are axial vectors**

**12. When a particle performs a non uniform circular motion it has a centripetal acceleration and a tangential acceleration. directed along the tangent**

**13. As and are at right angles, the net acceleration**

**14. For a U.C.M. a**

_{T}= 0 or α = 0. No work is done in U.C.M.**15. Motion in a Vertical circle:**

**When a body moves in a vertical circle,**

**· The tension (if string is used) or normal reaction at any point P is given by**

**· Tension at the lowest point (A) is maximum.**

**· Tension at the highest point (B) is minimum.**

**· The minimum horizontal velocity that should be given to the body at the bottom (A) to complete the vertical loop is given by**

**· Minimum speed required at**

**· Velocity at C or D =**

**· Tension at C or D (ends of the horizontal diameter)**

**· K.E. at A – K.E. at B = 2 mgr**

**· T**

_{A}- T_{B}= 6 mg**16. For looping a loop of radius r, the minimum height from which the body should be released is given by**

**17. The expressions, are used in the following cases:**

**(i) Bucket full of water rotated in a vertical circle.**

**(ii) Motor cyclist riding in a vertical circle in a hollow sphere.**

**18. Conical Pendulum:**

**(i) If T is the tension in the string, then**

**(ii)**

**Where T is the period of the conical pendulum.**

**(iii) The period of a conical pendulum is less than the period of a simple pendulum of the same length.**

**19. Useful Points:**

**(i) Newton’s laws of motion are valid in an inertial frame of reference. In this frame, we consider the real forces.**

**(ii) A frame of reference which is moving with an acceleration w.r.t. the system of fixed stars is called a non-inertial frame or accelerated frame of reference. In this frame, Newton’s laws of motion are not valid. To apply Newton’s laws of motion to situations in non inertial frames, we consider the fictitious or pseudo forces. Centrifugal force is a pseudo force.**

**(iii) Centripetal force and centrifugal force do not form an action-reaction pair.**

**(iv) For a speed breaker,**

**(v) In banked roads, the horizontal components R sin θ provides the necessary centripetal force. While the vertical component R cos θ balances the weight (mg) of the car.**

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### Circular Motion

**Important Information**

**When a body moves along a circular path with uniform speed, it is said to perform a uniform circular motion (U.C.M.).**

**In U.C.M.**

**1. Angular speed of a particle,**

**Where θ is the angular displacement in time‘t’. T is the period of revolution of the particle performing a U.C.M. and n is the frequency of revolution i.e. no .of revolutions completed by the particle per second. S.I. unit of ω is rad/s.**

**Angular Velocity (ω): It is the rate of change of angular displacement w.r.t. time.**

**2. The linear speed of a particle v = rω where r is the radius of the circle.**

**3. S.I. unit of α is rad/sec**

^{2}**Linear acceleration (a) = r α.**

**4. In U.C.M. the acceleration is always directed along the radius, towards the centre of the circle. It is called radial or centripetal acceleration. The magnitude of C.P. acceleration is . If m is the mass of the body performing U.C.M., then the centripetal force acting upon it is . It is also given by**

**The radial acceleration**

**5. If the angular acceleration α is constant then for accelerated circular motion,**

**(i)**

**(ii)**

**(iii)**

**Where ω**

_{0}is the angular speed of the particle at time t = 0 and ω is the angular speed of the particle after time‘t’.**6. Banking of Roads: For a vehicle moving along a circular track of radius r, banked at an angle θ, the maximum speed limit for the safety of the vehicle is given by**

**V is also known as critical speed. In the case of a train, the elevation of the outer rail above the inner rail is given by**

**h = ℓ sin θ.**

**Where is the distance between the rails.**

**For a metre gauge railway,**

**7. For a vehicle moving along a horizontal curve of radius r, (unbanked circular road), the C.P. force is provided by the friction. The maximum safe speed (v) is calculated by using the relation**

**Where μ is the coefficient of friction between the tyres of the car and the surface of the road.**

**8. A cyclist, moving with a speed v, along a horizontal curved road of radius r, has to lean inwards to keep his balance. His angle of inclination (θ) with the vertical is given by**

**9.**

**10.**

**11. Direction of are given by right hand thumb rule.**

**are axial vectors**

**12. When a particle performs a non uniform circular motion it has a centripetal acceleration and a tangential acceleration. directed along the tangent**

**13. As and are at right angles, the net acceleration**

**14. For a U.C.M. a**

_{T}= 0 or α = 0. No work is done in U.C.M.**15. Motion in a Vertical circle:**

**When a body moves in a vertical circle,**

**· The tension (if string is used) or normal reaction at any point P is given by**

**· Tension at the lowest point (A) is maximum.**

**· Tension at the highest point (B) is minimum.**

**· The minimum horizontal velocity that should be given to the body at the bottom (A) to complete the vertical loop is given by**

**· Minimum speed required at**

**· Velocity at C or D =**

**· Tension at C or D (ends of the horizontal diameter)**

**· K.E. at A – K.E. at B = 2 mgr**

**· T**

_{A}- T_{B}= 6 mg**16. For looping a loop of radius r, the minimum height from which the body should be released is given by**

**17. The expressions, are used in the following cases:**

**(i) Bucket full of water rotated in a vertical circle.**

**(ii) Motor cyclist riding in a vertical circle in a hollow sphere.**

**18. Conical Pendulum:**

**(i) If T is the tension in the string, then**

**(ii)**

**Where T is the period of the conical pendulum.**

**(iii) The period of a conical pendulum is less than the period of a simple pendulum of the same length.**

**19. Useful Points:**

**(i) Newton’s laws of motion are valid in an inertial frame of reference. In this frame, we consider the real forces.**

**(ii) A frame of reference which is moving with an acceleration w.r.t. the system of fixed stars is called a non-inertial frame or accelerated frame of reference. In this frame, Newton’s laws of motion are not valid. To apply Newton’s laws of motion to situations in non inertial frames, we consider the fictitious or pseudo forces. Centrifugal force is a pseudo force.**

**(iii) Centripetal force and centrifugal force do not form an action-reaction pair.**

**(iv) For a speed breaker,**

**(v) In banked roads, the horizontal components R sin θ provides the necessary centripetal force. While the vertical component R cos θ balances the weight (mg) of the car.**

### HSC Books

**Physics :-**

Government Sanctioned Text Book (G.T.B)

**The latest edition has completely solution of the unsolved part of the Government Sanctioned Textbook (G.T.B). Moreover they have provided with errors in the questions and answers of G.T.B**

Sheth Publications – Problems in Physics [For Numerical Problems]

Uttams Papers With Solutions – It gives complete solutions of Latest Previous Years Board Papers . Also It has Specimen Papers too.

Navneet Log Table Book – It is required to solved difficult problems which has lengthy calculations. Logarithm tables and many tables are requires for preparation of HSC

**Chemistry :-**

Government Sanctioned Text Book (G.T.B)

**The latest edition has completely solution of the unsolved part of the Government Sanctioned Textbook (G.T.B). Moreover they have provided with errors in the questions and answers of G.T.B**

**Mathematics :-**

**The latest edition has completely solution of the unsolved part of the Government Sanctioned Textbook (G.T.B). Moreover they have provided with errors in the questions and answers of G.T.B**

**Biology :-**

**G.T.B**is a must

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### >HSC Books

>

**Physics :-**

Government Sanctioned Text Book (G.T.B)

Sheth Publications – Problems in Physics [For Numerical Problems]

Uttams Papers With Solutions – It gives complete solutions of Latest Previous Years Board Papers . Also It has Specimen Papers too.

Navneet Log Table Book – It is required to solved difficult problems which has lengthy calculations. Logarithm tables and many tables are requires for preparation of HSC

**Chemistry :-**

**Mathematics :-**

**Biology :-**

**G.T.B**is a must

### MCQ Books For MHT-CET

**Physics :-**

Marvel Publications

Nikita Publications ( Famously known Pradnya )

Target Publications

Navneet Publications

Vidyabhartee Publications

Uttam Publications

**Chemistry :-**

Himalaya Publishing House

Sheth Publications ( Famously known Scholars )

Marvel Publications

Nikita Publications ( Famously known Pradnya )

Vidyabhartee Publications

**Mathematics :-**

**Biology:-**

You should try solve at least 2-3 completely for a better score in MHT-CET. These are not sanctioned books but these are relevant books for strengthening your preparation

Facebook Fan Page

https://www.facebook.com/pages/hscmhtcetblogspotcom/284426244901089

### >MCQ Books For MHT-CET

>

**Physics :-**

Marvel Publications

Nikita Publications ( Famously known Pradnya )

Target Publications

Navneet Publications

Vidyabhartee Publications

Uttam Publications

**Chemistry :-**

Himalaya Publishing House

Sheth Publications ( Famously known Scholars )

Marvel Publications

Nikita Publications ( Famously known Pradnya )

Vidyabhartee Publications

**Mathematics :-**

**Biology:-**

You should try solve at least 2-3 completely for a better score in MHT-CET. These are not sanctioned books but these are relevant books for strengthening your preparation

### Physics Chapter Wise Papers

http://www.patshala.com/mhcet/home/phy/cirmot.html

2. Gravitation

http://www.patshala.com/mhcet/home/phy/gravitation.html

3. Rotational Motion

http://www.patshala.com/mhcet/home/phy/rotmot.html

4. Oscillations

http://www.patshala.com/mhcet/home/phy/oscillation.html

5. Elasticity

http://www.patshala.com/mhcet/home/phy/elasticity.html

6. Surface Tension

http://www.patshala.com/mhcet/home/phy/surten.html

7. Wave Motion

http://www.patshala.com/mhcet/home/phy/wavmot.html

8. Stationary Waves

http://www.patshala.com/mhcet/home/phy/stawav.html

9. Kinetic Theory Of Gases

http://www.patshala.com/mhcet/home/phy/ktg.html

10. Radiation

http://www.patshala.com/mhcet/home/phy/radiation.html

11. Physics Entire Paper 1

http://www.patshala.com/mhcet/eng/test/phy1.html

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### MHT-CET Papers By Learn Hub