eSaral - JEE | NEET | Class 8-10 Exam Prep App

If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5 × 107 ms–1,

Question: If the photon of the wavelength 150 pm strikes an atom and one ofits inner bound electrons is ejected out with a velocity of 1.5 107ms1, calculate the energy with which it is bound to the nucleus. Solution: Energy of incident photon $(E)$ is given by, $E=\frac{h c}{\lambda}$ $=\frac{\left(6.626 \times 10^{-34} \mathrm{Js}\right)\left(3.0 \times 10^{8} \mathrm{~ms}^{-1}\right)}{\left(150 \times 10^{-12} \mathrm{~m}\right)}$ $=1.3252 \times 10^{-15} \mathrm{~J}$ $\simeq 13.252 \times 10^...

A metre stick is balanced on a knife edge at its centre.

Question: A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the metre stick? Solution: LetWandWbe the respective weights of the metre stick and the coin. The mass of the metre stick is concentrated at its mid-point, i.e., at the 50 cm mark. Mass of the meter stick $=m^{\prime}$ Mass of each coin,m= 5 g When the coins are placed 12 cm away ...

The angle of elevation of the top of the building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°.

Question: The angle of elevation of the top of the building from the foot of the tower is 30 and the angle of elevation of the top of the tower from the foot of the building is 60. If the tower is 50 m high, find the height of the building. Solution: $\mathrm{PQ}=50$ metres is the height of the tower. Let $\mathrm{AB}=\mathrm{h}$ metres be the height of the building. Angle of elevation of the top of the building from the foot of the tower $=30^{\circ}$, i.e., $\angle \mathrm{AQB}=30^{\circ}$. An...

From a uniform disk of radius R, a circular hole of radius R/2 is cut out.

Question: From a uniform disk of radiusR, a circular hole of radiusR/2 is cut out. The centre of the hole is atR/2 from the centre of the original disc. Locate the centre of gravity of the resulting flat body. Solution: R/6; from the original centre of the body and opposite to the centre of the cut portion. Mass per unit area of the original disc $=\sigma$ Radius of the original disc $=R$ Mass of the original disc, $M=\pi R^{2} \sigma$ The disc with the cut portion is shown in the following figu...

Differentiate between the following:

Question: Differentiate between the following: (a) Diffusion and Osmosis (b) Transpiration and Evaporation (c) Osmotic Pressure and Osmotic Potential (d) Imbibition and Diffusion (e) Apoplast and Symplast pathways of movement of water in plants. (f) Guttation and Transpiration. Solution: (a)Diffusion and osmosis (b) Transpiration and evaporation (c) Osmotic pressure and osmotic potential (d)Imbibition and diffusion (e)Apoplast and symplast pathways of movement of water in plants (f) Guttation an...

A statue, 1.6 m tall, stands on the top of pedestal.

Question: A statue, 1.6 m tall, stands on the top of pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 and from the same point the angle of elevation of the top of the pedestal is 45. Find the height of the pedestal. Solution: In the figure, DC represents the statue and BC represents the pedestal. Now, in right $\triangle \mathrm{ABC}$, we have $\frac{\mathbf{A B}}{\mathbf{B C}}=\cot 45^{\circ}=1$ $\Rightarrow \frac{\mathbf{A B}}{\mathbf{h}}=1$ $\Rightar...

To maintain a rotor at a uniform angular speed of 200 rad s–1,

Question: To maintain a rotor at a uniform angular speed of $200 \mathrm{rad} \mathrm{s}^{-1}$, an engine needs to transmit a torque of $180 \mathrm{Nm}$. What is the power required by the engine? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is 100 % efficient. Solution: Angular speed of the rotor, $\omega=200 \mathrm{rad} / \mathrm{s}$ Torque required, $\mathrm{T}=180 \...

The ejection of the photoelectron from the silver metal in the photoelectric

Question: The ejection of the photoelectron from the silver metal in the photoelectric effect experiment can be stopped by applying the voltage of 0.35 V when the radiation 256.7 nm is used. Calculate the work function for silver metal. Solution: From the principle of conservation of energy, the energy of an incident photon (E) is equal to the sum of the work function (W0) of radiation and its kinetic energy (K.E) i.e $E=W_{0}+K \cdot E$ $\Rightarrow W_{0}=E-K \cdot E$ Energy of incident photon ...

From a point on the ground the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively.

Question: From a point on the ground the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45 and 60 respectively. Find the height of the tower. Solution: PQ = 20 m is the height of the building. Let PR = h metres be the height of the transmission tower. P is the bottom and R is the top of the transmission tower. $\angle \mathrm{POQ}=45^{\circ}$ and $\angle \mathrm{ROQ}=60^{\circ}$ From $\Delta \mathrm{OPQ}$, $\Rightarrow \frac{\mathbf...

A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm.

Question: A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping. Solution: Mass ofthe hollow cylinder,m= 3 kg Radius of the hollow cylinder,r= 40 cm = 0.4 m Applied force,F= 30 N The moment of inertia of the hollow cylinder about its geometric axis: $I=m r^{2}$ $=3 \times(0.4)^{2}=0.48 \mathr...

(a) A child stands at the centre of a turntable with his two arms outstretched.

Question: (a) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value? Assume that the turntable rotates without friction. (b) Show that the childs new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase i...

A 1.5 m tall boy is standing at some distance from a 30 m tall building

Question: A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30 to 60 as he walks towards the building. Find the distance he walked towards the building. Solution: PQ = 30 m is the height of the building. OA = 1.5 m is the height of the boy. Its first position is at OA OR is horizontal line through the position of the eye at O. $\angle \mathrm{POR}=30^{\circ}$ (Given) The second position of the b...

Explain why pure water has the maximum water potential.

Question: Explain why pure water has the maximum water potential. Solution: Water potential quantifies the tendency of water to move from one part to the other during various cellular processes. It is denoted by the Greek letter Psi or Ψ. The water potential of pure water is always taken as zero at standard temperature and pressure. It can be explained in terms of the kinetic energy possessed by water molecules. When water is in liquid form, the movement of its molecules is rapid and constant. P...

Describe the role played by protein pumps during active transport in plants.

Question: Describe the role played by protein pumps during active transport in plants. Solution: In plant cells, active transport occurs against the concentration gradient, i.e., from a region of lower concentration to a region of higher concentration. The process of active transport involves specific protein pumps. The protein pumps are made up of specific proteins called trans-membrane proteins. These pumps first make a complex with the substance to be transported across the membrane, using th...

A kite is flying at a height of 60 m above the ground.

Question: A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60. find the length of the string, assuming that there is no slack in the string. Solution: $P$ is the position of the kite. Its height from the point $Q$ (on the ground) $=P Q=60 \mathrm{~m}$ Let $O P=\ell$ be the length of the string. $\angle \mathrm{POQ}=60^{\circ}$ (Given) Now, $\frac{\mathbf{P Q}}{\mat...

What are porins? What role do they play in diffusion?

Question: What are porins? What role do they play in diffusion? Solution: Porins are types of proteins which form pores of large sizes in the outer membranes of plastids such as chloroplast, mitochondria and the membranes in bacteria. They help in facilitating the passive transport of small-sized protein molecules....

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s–1.

Question: A solid cylinder of mass $20 \mathrm{~kg}$ rotates about its axis with angular speed $100 \mathrm{rad} \mathrm{s}^{-1}$. The radius of the cylinder is $0.25 \mathrm{~m}$. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis? Solution: Mass ofthe cylinder,m= 20 kg Angular speed, $\omega=100 \mathrm{rad} \mathrm{s}^{-1}$ Radius of the cylinder, $r=0.25 \mathrm{~m}$ The moment of inertia of the so...

The angle of elevation of the top of a tower from a point on the ground,

Question: The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30. Find the height of the tower. Solution: In right ABC, AB = height of the tower and point C is 30m away from the foot of the tower, $\therefore \quad \mathrm{AC}=30 \mathrm{~m}$ $\operatorname{Now} \frac{\mathbf{A B}}{\mathbf{A C}}=\tan 30^{\circ}$ $\Rightarrow \frac{\mathbf{h}}{\mathbf{3 0}}=\frac{1}{\sqrt{\mathbf{3}}}$ $\left[\because \tan 30^{\circ}=\frac{\ma...

A contractor plans to install two slides for the children to play in a park.

Question: A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she perfers to have a slide whose top is at a height of 1.5 m and is inclinded at an angle of 30 to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m, and inclined at an angle of 60 to the ground. What should be the length of the slide in each case? Solution: In figure, $\ell_{1}$ is the length of the slide made for children be...

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere,

Question: Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time? Solution: Letmandrbe the respective masses of the hollow cylinder and the solid sphere. The moment of inertia of the hollow cylinder about its standard axi...

What are the factors affecting the rate of diffusion?

Question: What are the factors affecting the rate of diffusion? Solution: Diffusion is the passive movement of substances from a region of higher concentration to a region of lower concentration. Diffusion of substances plays an important role in cellular transport in plants. Rate of diffusion is affected by concentration gradient, membrane permeability, temperature, and pressure. Diffusion takes place as long as there is a difference between the concentrations of a substance across a barrier. H...

A tree breaks due to storm and the broken part bends so that the top of the trees touches the ground making an angle of 30° with the ground.

Question: A tree breaks due to storm and the broken part bends so that the top of the trees touches the ground making an angle of 30 with the ground. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree. Solution: Let tree is broken at A and its top is touching the ground at B. Now, in right $\triangle \mathrm{AOB}$, we have $\frac{\mathbf{A O}}{\mathbf{O B}}=\tan 30^{\circ}$ $\Rightarrow \frac{\mathbf{A 0}}{\mathbf{8}}=\frac...

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground

Question: A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is 30 (see fig.). Solution: AC = 20 m is the length of the rope. Let AB = h metres be the height of the pole $\angle \mathrm{ACB}=30^{\circ}($ Given $)$ Now, $\frac{\mathbf{A B}}{\mathbf{A C}}=\sin \mathbf{3 0}^{\circ}=\frac{\mathbf{1}}{\mathbf{2}}$ $\frac{h}{20}=\frac{1}{2}$ $h=1...

Neon gas is generally used in the sign boards.

[question] Question. Neon gas is generally used in the sign boards. If it emits strongly at 616 nm, calculate (a) the frequency of emission, (b) distance traveled by this radiation in 30 s (c) energy of quantum and (d) number of quanta present if it produces 2 J of energy. [/question] [solution] Solution: Wavelength of radiation emitted $=616 \mathrm{~nm}=616 \times 10^{-9} \mathrm{~m}$ (Given) (a) Frequency of emission $(v)$ $v=\frac{c}{\lambda}$ Where, $c=$ velocity of radiation $\lambda=$ wav...

Proteins have primary structure.

[question] Question. Proteins have primary structure. If you are given a method to know which amino acid is at either of the two termini (ends) of a protein, can you connect this information to purity or homogeneity of a protein? [/question] [solution] Solution: Yes, if we are given a method to know the sequence of proteins, we can connect this information to the purity of a protein. It is known that an accurate sequence of a certain amino acid is very important for the functioning of a protein....

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