Find the reading of the spring balance shown in figure.
Question: Find the reading of the spring balance shown in figure. The elevator is going up with an acceleration of $g / 10$, the pulley and the string are light and the pulley is smooth. Solution:...
Read More →A person is standing on a weighing machine placed
Question: A person is standing on a weighing machine placed on the floor of an elevator. The elevator starts going up with some acceleration, moves with uniform velocity for a while and finally decelerates to stop. The maximum and the minimum weights recorded are $72 \mathrm{~kg}$ and $60 \mathrm{~kg}$. Assuming that the magnitudes of the acceleration and the deceleration are the same, find (a) the true weight of the person and $(b)$ the magnitude of the acceleration. Take $g=9.9 \mathrm{~m} / \...
Read More →Solve this following
Question: Find the adjoint of the given matrix and verify in each case that $A .(\operatorname{adj} A)=(\operatorname{adj} A)=m|A| . I$ $\left[\begin{array}{ccc}9 7 3 \\ 5 -1 4 \\ 6 8 2\end{array}\right]$ Solution:...
Read More →A pendulum bob of mass
Question: A pendulum bob of mass $50 \mathrm{~g}$ is suspended from the ceiling of an elevator. Find the tension in the string if the elevator (a) goes up with acceleration $1.2 \mathrm{~m} / \mathrm{s}^{2}$, (b) goes up with deceleration $1.2 \mathrm{~m} / \mathrm{s}^{2}$, (c) goes up with uniform velocity, (d) goes down with acceleration $1.2 \mathrm{~m} / \mathrm{s}^{2}$, (e) goes down with deceleration $1.2 \mathrm{~m} / \mathrm{s}^{2}$ and (f) goes down with uniform velocity. Solution:...
Read More →The elevator shown in figure is descending
Question: The elevator shown in figure is descending with an acceleration of $2 \mathrm{~m} / \mathrm{s}^{2}$. The mass of the block A is $0.5 \mathrm{~kg}$. What force is exerted by the block $A$ on the block B? Solution:...
Read More →A man has fallen into a ditch of width d
Question: A man has fallen into a ditch of width $d$ and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure. Show that the force (assumed equal for both the friends) exerted by each friend on the road increases as the man moves up. Find the force when the man is at a depth $h$. Solution: (a)...
Read More →A small block B is placed on another block A of
Question: A small block B is placed on another block A of mass $5 \mathrm{~kg}$ and length $20 \mathrm{~cm}$. Initially the block B is near the right end of block A. A constant horizontal force of $10 \mathrm{~N}$ is applied to the block A. All the surfaces are assumed frictionless. Find the time elapsed before the block $B$ separates from $A$. Solution:...
Read More →Find the adjoint of the given matrix and verify
Question: Find the adjoint of the given matrix and verify in each case that $A$. $(\operatorname{adj} A)=(\operatorname{adj} A)=m|A| . I$. $\left[\begin{array}{lll}0 1 2 \\ 1 2 3 \\ 3 1 1\end{array}\right]$ Solution: Ans. $\left[\begin{array}{ccc}-1 1 -1 \\ 8 -6 2 \\ -5 3 -1\end{array}\right]$...
Read More →Both the springs shown in figure are unstretched.
Question: Both the springs shown in figure are unstretched. If the block is displaced by a distance $x$ and released, what will be the initial acceleration? Solution:...
Read More →A particle of mass 0.3 kg is subjected to a force
Question: A particle of mass $0.3 \mathrm{~kg}$ is subjected to a force $\mathrm{F}=-\mathrm{k} \mathrm{x}$ with $\mathrm{k}=15 \mathrm{~N} / \mathrm{m}$. What will be its initial acceleration if it is released from a point $x=20 \mathrm{~cm}$ ? Solution:...
Read More →Raindrops of radius
Question: Raindrops of radius $1 \mathrm{~mm}$ and mass $4 \mathrm{mg}$ are falling with a speed of $30 \mathrm{~m} / \mathrm{s}$ on the head of a bald person. The drops splash on the head and come to rest. Assuming equivalently that the drops cover a distance equal to their radii on the head, estimate the force exerted by each drop on the head. Solution:...
Read More →Two blocks A and B of mass mA and
Question: Two blocks $\mathrm{A}$ and $\mathrm{B}$ of mass $\mathrm{mA}$ and $\mathrm{mB}$ respectively are kept in contact on a frictionless table. The experimenter pushes the block A from behind so that the blocks accelerate. If the block A exerts a force $F$ on the block B, what is the force exerted by the experimenter on A? Solution:...
Read More →Find the adjoint of the given matrix and verify in each case that
Question: Find the adjoint of the given matrix and verify in each case that $A .(\operatorname{adj} A)=(\operatorname{adj} A)=m|A| . I$. $\left[\begin{array}{ccc}3 -1 1 \\ -15 6 -5 \\ 5 -2 2\end{array}\right]$ Solution:...
Read More →A particle of mass 50 g moves on a straight line.
Question: A particle of mass $50 \mathrm{~g}$ moves on a straight line. The variation of speed with time is shown in figure. Find the force acting on the particle at $t=2,4$ and 6 seconds. Solution:...
Read More →Two blocks of equal mass m are tied to each other
Question: Two blocks of equal mass $m$ are tied to each other through a light string. One of the blocks is pulled along the line joining them with a constant force F. Find the tension in the string joining the blocks. Solution:...
Read More →Find the adjoint of the given matrix and verify in each case that
Question: Find the adjoint of the given matrix and verify in each case that $A .(\operatorname{adj} \mathrm{A})=(\operatorname{adj} \mathrm{A})=\mathrm{m}|\mathrm{A}| . \mathrm{I} .\left[\begin{array}{ccc}1 -1 2 \\ 3 1 -2 \\ 1 0 3\end{array}\right]$ Solution:...
Read More →A block of mass 0.2 kg is suspended from the ceiling
Question: A block of mass $0.2 \mathrm{~kg}$ is suspended from the ceiling by a light string. A second block of mass $0.3 \mathrm{~kg}$ is suspended from the first block through another string. Find the tensions in the two strings. Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$. Solution:...
Read More →In a TV picture tube electrons are ejected
Question: In a TV picture tube electrons are ejected from the cathode with negligible speed and reach a velocity of $5 \times 10^{6} \mathrm{~m} / \mathrm{s}$ in travelling one centimeter. Assuming straight line motion, find the constant force exerted on the electron. The mass of the electron is $9.1 \times 10^{-31} \mathrm{~kg}$. Solution:...
Read More →A car moving at 40 km/h is to be stopped by applying brakes
Question: A car moving at $40 \mathrm{~km} / \mathrm{h}$ is to be stopped by applying brakes in the next $4.0 \mathrm{~m}$. If the car weighs $2000 \mathrm{~kg}$, what average force must be applied on it? Solution:...
Read More →Find the adjoint of the given matrix and verify
Question: Find the adjoint of the given matrix and verify in each case that $A .(\operatorname{adj} A)=(\operatorname{adj} A)=m|A| .1 .\left[\begin{array}{cc}\operatorname{Cos} \alpha \sin \alpha \\ \sin \alpha \cos \alpha\end{array}\right]$ Solution: Hence Proved Ans. $\left[\begin{array}{cc}\cos \alpha -\sin \alpha \\ -\sin \alpha \cos \alpha\end{array}\right]$...
Read More →A block of mass 2 kg placed on a long frictionless horizontal table
Question: A block of mass $2 \mathrm{~kg}$ placed on a long frictionless horizontal table is pulled horizontally by a constant force $F$. It is found to move $10 \mathrm{~m}$ in the first two seconds. Find the magnitude of $F$. Solution:...
Read More →Find the adjoint of the given matrix and verify in each case
Question: Find the adjoint of the given matrix and verify in each case that $A .(\operatorname{adj} A)=(\operatorname{adj} A)=m|A| \cdot I .\left[\begin{array}{cc}3 -5 \\ -1 2\end{array}\right]$ Solution:...
Read More →Find the adjoint of the given matrix and verify in each case that
Question: Find the adjoint of the given matrix and verify in each case that $A .(\operatorname{adj} A)=(\operatorname{adj} A)=m|A| . I$. $\left[\begin{array}{ll}2 3 \\ 5 9\end{array}\right]$ Solution: Ans. $\left[\begin{array}{cc}9 -3 \\ -5 2\end{array}\right]$...
Read More →The geostationary orbit of the earth is at a distance
Question: The geostationary orbit of the earth is at a distance of about $36000 \mathrm{~km}$ from the earth's surface. Find the weight of $120 \mathrm{~kg}$ equipment placed in a geostationary satellite. The radius of the earth is $6400 \mathrm{~km}$. Solution:...
Read More →The average separation between the proton and the electron
Question: The average separation between the proton and the electron in a hydrogen atom in ground state is $5.3 \times 10^{-11} \mathrm{~m}$. (a) Calculate the Coulomb force between them at this separation (b) When the atom goes into its first excited state the average separation between the proton and the electron increases to four times its value in the ground state. What is the Coulomb force in this state? Solution:...
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