# 1st Year Physics Important Numericals

1. If one of the rectangular components of a force of 100 N is 50 N, find the other component.

2. Two bodies A and B are attached to the ends of a string passing over a frictionless pulley such that the masses hang vertically. If the mass of one body is 96kg, find the mass of second body, which moves downward with an acceleration of 0.2 m/s2 and the tension in the string. (g = 9.8 m/s2)

3. An artillery cannon is pointed upward at an angle 35° with respect of horizontal and fires a projectile with an initial velocity of 200m/s. If the air resistance is negligible, find the maximum height reached by the projectile and the range of the projectile.

4. Two vectors have magnitudes 4 and 5 units. The angle between them is 30°. Taking the first vector along x-axis, calculate the magnitude and the direction of the resultant.

5. Given that , find , , and the angle between.

6. A 100 gm bullet is fired into a 12kg block which is suspended by a long cord. If the bullet is embedded in the block and the block and the block rises by 5cm. What was the speed of the bullet?

7. The radius of the moon is 27% of the earth’s radius and its mass is 1.2% of the earth’s mass. Find the acceleration due to gravity on the surface of the moon. How much does a 980 N body weigh there.

8. Find the value of P for which the following vectors are perpendicular to each other.

9. A boy throws a ball vertically upward with a speed of 25m/s. On the way down, it is caught at a point 5m above the ground. How fast was it coming down at this point? How long did the trip take?

10. A string 1m long would break when its tension is 69.6N. Find the greatest speed at which a ball of mass 2kg can be whirled with the string in a vertical circle.

11. A ladder rests against a smooth wall at an angle of 60° with the ground. The ladder weighs 200 N and its centre of gravity is at one thirds of its length from the base. Determine the frictional force, which prevents the ladder from slipping, and the coefficient of static friction.

12. If two vectors are such that A = 3 and B = 2 and = 4, evaluate and .

13. If find a unit vector parallel to .

14. A mortar shell is fired at ground level target 490m away with an initial velocity of 98m/s. Find the two possible values of the launch angle. Calculate the minimum time to hit the target.

15. Find how deep from the surface of earth a point where earth a point is where the acceleration due to gravity is half the value on the earth’s surface.

16. Given . Find the magnitude of vectors , and .

17. A minibus starts moving from the position of rest at a bust stop with a uniform acceleration during the 10th minute of its motion it covers a distance of 95m. Calculate its acceleration and the total distance it covers in 10 minutes.

18. Calculate the work done by a force given by in displacing a body from the position A to the position B. The position vectors A and B are

1. A body of 0.5kg attached to a spring is displaced from its equilibrium position and is released. If spring constant K is 50N/m, find the time period and the frequency.

2. A car has siren sounding 2KHz tone. What frequency will be detected by stationary listener as the car is approaching him at 80km/h. (speed of sound = 1200 km/h).

3. Calculate the speed of sound in air at atmospheric pressure P = 1.01 x 105 N/m2, taking g = 1.40 and r = 1.2 kg/m3.

4. Calculate the length of second’s Pendulum at a place where g = 10.0 m/s2.

5. When mass m is hung on a vertical spring, it stretches through 6cm. Determine its period of vibration if its is pulled down a little and released.

6. A guitar string has a linear density of 7.16 gm/m and is under tension of 152 N. the fixed supports of the string are 89.4 cm apart. If its vibrates in three segments. Calculate the speed, the wavelength and the frequency of the standing wave.

7. Calculate the length of second’s pendulum on the surface of moon where the acceleration due to gravity is 0.167 times that on the earth’s surface.

8. A source of sound and a listener are moving towards each other with velocities, which are 0.5 time, and 0.2 time the speed of sound respectively. If the source is emitting 2KHz tone. Calculate the frequency heard by the listener.

9. A stationary wave is set in a 1.5 metre long string fixed at both ends. The string vibrates in five segments when driven by a frequency of 100 Hz. Calculate the wavelength and the fundamental frequency.

1. How many fringes will pass a reference point if the movable mirrors of the Michelson’s Interferometer are moved by 0.08 mm? The wavelength of light used is 5800 A°.

2. A green light of wavelength 5400 A° is diffracted by a diffraction grating having 2000 lines/cm. Compute the angular deviation of the third order image.

3. Find the distance at which an object should be placed in front of a convex lens of focal length 20 cm to obtain an image of double its size.

4. If the radius of 14th ring is 1mm and the radius of curvature of the lens 126 mm. calculate the wavelength of light.

5. Red light falls normally on a diffraction grating ruled 4000 lines /cm and the second order image is diffracted 34° from the normal. Compute the wavelength of red light in angstroms.

6. In a compound microscope, the focal lengths of the objective and eyepiece are 0.8cm and 2.5cm respectively. The real image is formed by the objective is 16cm from it. Determine the Magnifying power if the eyepiece is held close to the eyepiece and the image is formed 25cm from the eyepiece.

7. Interference fringes were produced by two slits on a screen 0.8m from them when the light of wavelength 5.8 x 10m was used. If the separation between the first and fifth bright fringe is 2.5 mm. Calculate the separation of the two slits.

8. If the radius of 10th ring is 0.5mm when the light o 6.00 x 10-7 m is used. What is the radius of curvature of the lens used?