Q: A man is standing at a distance of 500 m from a building. He notes that angle of elevation of the top of the building is 3.6∘. Find the height of the building. Neglect the height of the man and take π=3.14

tanθ=500h h=500tan(3.6) =500×0.0629 =31.457 h≈31.46 m

Q: A Smuggler in a hindi film is running with a bag 0.3 m×0.2 m×0.2 m in dimension. The bag is supposed to be completely filled with gold. Do you think than the director of the film made a technical mistake there? Density of gold is 19.6 g/cc.

Dimension of bag valume densihy nass of gold full =0.3×0.2×0.2=0.3×0.2×0.2=.012 m3=19.6cm3g=19600m3kg=19600×0.012=235.2 kg

Q: The area of a regular octagon of side length a is A. (a) Find the time rate of change of area of the octagon if its side length is being increased at a constant rate of βm/s. Is the time rate of change of area of the octagon constant with time? (b) Find the approximate change in area of the octagon as the side length is increased from 2.0 m to 2.001 m

(a) 4(2+1)aβ. No, it is not a constant (b) 0.0019 m2

Q: The volume flow rate Q( in m3s−1) of a liquid through pipe having diameter d is related to viscosity of water ' η ' (unit Pascal. s ) and the pressure gradient along the pipe dxdP [pressure gradient dxdP is rate of change of pressure per unit length along the pipe], by a formula of the form Q=kηadb(dxdP)c Where K is a dimensionless constant. Find a,b and c.

[Q]=[L3T−1] [n]=[ML3T−1] [d]=[L] [dxdP]=[ML−2T−2] a=−1;b=4;c=1

Q: In the following expression V and g are speed and acceleration respectively. Find the dimensional formulae of a and b ∫g−bV2VdV=a

dag−dabv2=L2T−2 da.g =L2T−2 [a]=L;[b]=L−1

Q: A particle of mass m is given an initial speed V0. It experiences a retarding force that is proportional to the speed of the particle (F=aV).a is a constant. (a) Write the dimensional formula of constant a. (b) Using dimensional analysis, derive a formula for stopping time (t) of the particle. Does your formula tell you how ' t ' depends on initial speed V0 ? What can you predict about the constant obtained in the formula?

(a) [a]=[V][F]=[MT−1] (b) let t=kaxmyV0z It can be shown that x=−1;y=1;z=0 ∴t=kam As per this expression, the time of motion is independent of initial speed ! This cannot be true. It must grow with V0. A large initial speed (V1) will need some non zero time to slow down to V2. After this the particle will take as much time to halt as it would take when projected with initial speed V2. The only way equation (a) can be sensible is by having k=∞.

Question 1

In an experiment mileage of a car was measured to be 24kmpl (Kilometer per liter of fuel consumed). After the experiment it was found that 4% of the fuel used during the experiment was leaked through a small hole in the tank. Calculate the actual mileage of the car after the tank was repaired.

Accepted Answer

25kmpl

Question 2

A man is standing at a distance of 500 m from a building. He notes that angle of elevation of the top of the building is 3.6∘. Find the height of the building. Neglect the height of the man and take π=3.14

Accepted Answer

tanθ=500h​
h=500tan(3.6)
=500×0.0629
=31.457
h≈31.46 m

Question 3

A Smuggler in a hindi film is running with a bag 0.3 m×0.2 m×0.2 m in dimension. The bag is supposed to be completely filled with gold. Do you think than the director of the film made a technical mistake there? Density of gold is 19.6 g/cc.

Accepted Answer

Dimension of bag valume  densihy  nass of  gold full ​=0.3×0.2×0.2=0.3×0.2×0.2=.012 m3=19.6cm3g​=19600m3kg​=19600×0.012=235.2 kg​

Question 4

A particle moves along the curve 6y=x3+2 Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.

Accepted Answer

The equation of the curve is given as, 6y=x3+2………..(1)Differentiating (1) both sides w.r.t.t​⇒6dtdy​=3x2dtdx​+0⇒2dtdy​=x2dtdx​…..(2)​ 
When, x=4⇒y=643+2​=666​=11[ from(1)]
when, x=(−4)⇒y=6(−4)3+2​=−662​=−331​ [from(1)]
Hence, the points required on the curve are (4,11) and (−4,3−31​).

Question 5

The area of a regular octagon of side length a is A.
(a) Find the time rate of change of area of the octagon if its side length is being increased at a constant rate of βm/s. Is the time rate of change of area of the octagon constant with time?
(b) Find the approximate change in area of the octagon as the side length is increased from 2.0 m to 2.001 m

Accepted Answer

(a) 4(​2+1)aβ. No, it is not a constant
(b) 0.0019 m2

Question 6

Spirit in a bowl evaporates at a rate that is proportional to the surface area of the liquid.
Initially, the height of liquid in the bowl is H0​. It becomes 2H0​​ in time t0​. How much more time will be needed for the height of liquid to become 4H0​​

Accepted Answer

dtdH​=kH
HdH​=kdt
t=2t0​​

Question 7

The amount of energy a car expends against air resistance is approximately given by
E=KADv2
where E is measured in Joules. K is a constant, A is the cross-sectional area of the car viewed from the front (in m2 ), D is the distance traveled (in m ), and v is the speed of the car (in m/s ). Julie wants to drive from Mumbai to Delhi and get good fuel mileage. For the following questions, assume that the energy loss is due solely to air resistance.
(a) Julie usually drives at a speed of 54Km/hr. How much more energy will she use if she drives 20% faster?
(b) Harshit drives a very large SUV car, and Julie drives a small car. Every linear dimension of Harshit's car is double that of Julie's car. Find the ratio of energy spent by Harshit's car to

Accepted Answer

(a) 44% higher (b) 4.84 (c) [ML−3]; Yes

Question 8

The volume flow rate Q( in m3s−1) of a liquid through pipe having diameter d is related to viscosity of water ' η ' (unit Pascal. s ) and the pressure gradient along the pipe dxdP​ [pressure gradient dxdP​ is rate of change of pressure per unit length along the pipe], by a formula of the form
Q=kηadb(dxdP​)c
Where K is a dimensionless constant. Find a,b and c.

Accepted Answer

[Q]=[L3T−1]
[n]=[ML3T−1]
[d]=[L]
[dxdP​]=[ML−2T−2]
a=−1;b=4;c=1

Question 9

The potential energy (U) of a particle can be expressed in certain case as U=2mr2A2​−rBMm​ Where m and M are mass and r is distance. Find the dimensional formulae for constants.

Accepted Answer

[A]=[M1L2T−1];[B]=[M−1L3T−2]

Question 10

In the following expression V and g are speed and acceleration respectively. Find the dimensional formulae of a and b
∫g−bV2VdV​=a

Accepted Answer

dag−dabv2​=L2T−2
da.g =L2T−2
[a]=L;[b]=L−1

Question 11

A Smuggler in a hindi film is running with a bag 0.3 m×0.2 m×0.2 m in dimension. The bag is supposed to be completely filled with gold. Do you think than the director of the film made a technical mistake there? Density of gold is 19.6 g/cc.

Accepted Answer

Calculate the mass of gold using − mass = volume × density. The gold in the bag will weigh 235.2 kg. How can a smuggler run with such a heavy bag!

Question 12

A particle of mass m is given an initial speed V0​. It experiences a retarding force that is proportional to the speed of the particle (F=aV).a is a constant.
(a) Write the dimensional formula of constant a.
(b) Using dimensional analysis, derive a formula for stopping time (t) of the particle. Does
your formula tell you how ' t ' depends on initial speed V0​ ? What can you predict about the constant obtained in the formula?

Accepted Answer

(a) [a]=[V][F]​=[MT−1]
(b) let t=kaxmyV0z​ It can be shown that x=−1;y=1;z=0
∴t=kam​
As per this expression, the time of motion is independent of initial speed ! This cannot be true. It must grow with V0​. A large initial speed (V1​) will need some non zero time to slow down to V2​. After this the particle will take as much time to halt as it would take when projected with initial speed V2​.
The only way equation (a) can be sensible is by having k=∞.

Filters

Filters

book

topic

difficulty

Solutions for Problems in Physics I for IIT JEE by Shashi Bhushan Tiwari

Found the solution, but did not understand the concept?

Ask my first question