Unit & Dimensions Questions and Answers

Assuming that the volume of a liquid flowing per second V through a cylindrical tube depends on i the pressure gradient P ii the radius of the tube and iii the coefficient of viscosity of liquid n Find by the method of dimension how it depends on these quantities

In an experiment the following observation s were recorded L 2 820 m M 3 00 kg I 0 087 cm Diameter D 0 041 cm Taking g 9 81 m s using the 4MgL formula Y the maximum TD 1 permissible error in Y is 1 7 96 2 4 56 3 6 50 4 8 42

Which of the following is correct A dimensionally incorrect equation may be correct A dimensionally correct equation must be physically correct Derived quantities may have dimensions in terms of the base quantities A unitless quantity may have a nonzero dimension

In an experiment four quantities a b c and d are measured with percentage error 1 2 3 and 4 respectively Quantity P is calculated as follows Flights cd a 7 error in Pis b 4 c 14 d 10

Question 9 Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity In one such system dimensions of different quantities are given in terms of a quantity X as follows position X speed X acceleration XP linear momentum X force X Then a a p 2B b p q r c q r a d p q r B

If the size of atom is in the range of 10 10 m to 10 m is scaled up to the tip of sharp pin assume tip of pin to be in the range of 10 6 to 10 5 m Roughly size of nucleus is NCERT Pg 20 1 0 1 A 2 0 01 A 3 0 001 4 10

Example 91 If two resistors of resistances R 4 0 5 and R 16 0 5 2 are connected i in series and ii ir parallel find the equivalent resistance in each case with limits of percentage error

A packet contains silver powder of mass 20 23 g 0 01 g Some of the powder of mass 5 75 g 0 0 01 g is taken out from it The mass of the powder left back is 1 14 48 g 0 00 g 2 14 48 0 02 g 3 14 5 g 0 1 g 4 14 5 g 0 2 g

In the formula X 3YZ X and Z have dimensions of capacitance and magnetic induction respectively What are the dimensions of Y in MKSQ system Q is the charge 1 M 7 0 2 M 14Q4 3 M 2 7 0 4 M 7 04

A body of mass 5 kg is suspended by a spring balance on a smooth inclined plane as shown in figure The reading of the spring balance will be g 10 m s 5 kg mmmm 30 50 N 25 N 25 3 N 25 2 N TTT

Two iron blocks of equal mass but having different surface area slide down on same inclined plane with coefficient of friction u If first block with surface area A experience a frictional force f then the second block with surface area 2A will experience frictional force f 712

In a screw gauge 5 complete rotation of the screw gauge it to move a linear distance of 0 25cm There are 100 circular scale divisions The thickness of a wire measured by this screw gauge gives a reading of 4 main scale division and 30 circular scale division Assuming negligible zero error the thickness of the wire is Question Type Single Correct Type 1 2 3 0 430 cm 0 215 cm 0 315 cm

Q A vernier callipers has its main scale of 10 cm equally divided into 200 equal parts Its vernier scale of 25 divisions coincides with 12 mm on the main scale The least count of the instrument is a 0 020 cm c 0 010 cm b 0 002 cm d 0 001 cm

A curved section of a road is banked for a speed V If there is no friction between road and tyres of the car then 1 car is more likely to slip at speeds higher than v than speeds lower than v car cannot remain in static equilibrium on the curved section 3 car will not slip when moving with speed v 4 None of the above

A flat plate moves normally with a speed vl towards a horizontal jet of water of uniform area of cross section The jet discharges water at the rate of volume V per second at a speed of v2 The density of water is p Assume that water splashes along the surface of the plate at right angles to the original motion The magnitude of the force acting on the plate due to the jet of water is A B pVv1 pV v V pV 21 22 P v V Un 2 V v 2

amusement park A machine in an consists of a cage at the end of one arm hinged at O The cage revolves along a vertical circle of radius r ABCOEFGH about its hinge O at constant linear speed v gr C The cage is so attached that the man of weight w standing on a weighing machine inside the cage is always vertical Then which of the following is correct a The reading of his weight on the machine is the same at all positions b The weight reading at A is greater than the weight read ing at Eby 2 w c The weight reading at G w d The ratio of the weight reading at E to that at A 0