BM Sharma Solutions for Chapter: Newton's Laws of Motion I, Exercise 7: DPP

A spring balance and a physical balance are kept in a lift. In these balances, equal masses are placed. Now, if the lift starts moving upwards with constant acceleration, then,

The masses of $10 \mathrm{kg}$ and $20 \mathrm{kg}$, respectively, are connected by a massless spring, as shown in the figure. A force of $200 \mathrm{N}$ acts on the $20 \mathrm{kg}$ mass. At the instant shown, the $10 \mathrm{kg}$ mass has acceleration $12 \mathrm{m} {\mathrm{s}}^{-2}$. What is the acceleration of $20 \mathrm{kg}$ mass?

An ideal spring is compressed and placed horizontally between a vertical fixed wall and a block, free to slide over a smooth horizontal tabletop as shown in the figure. The system is released from rest. The graph which represents the relation between the magnitude of the acceleration $a$ of the block and the distance $x$ travelled by it (as long as the spring is compressed) is,

Two blocks of masses $m_1$ and $m_2$, which are connected with a light string, are placed over a frictionless pulley. This set-up is placed over a weighing machine, as shown. Three combinations of masses $m_1$ and $m_2$ are used. In the first case, $m_1=$ $6 \mathrm{kg}$ and $m_2=2 \mathrm{kg}$, in second case, $m_1=5 \mathrm{kg}$ and $m_2=3 \mathrm{kg}$ and in the third case, $m_1=4 \mathrm{kg}$ and $m_2=4 \mathrm{kg}$. The masses are held stationary initially and then released. If the readings of the weighing machine after the release, in three cases, are $W_1, W_2$ and $W_3$, respectively, then,

A block $A$ of mass $m$ is attached at one end of a light spring and the other end of the spring is connected through a light string to another block $B$ of mass $2m$, as shown in the figure. $A$ is held and $B$ is in static equilibrium. Now, $A$ is released. The acceleration of $A$ just after that instant is $a$. In the next case, $B$ is held and $A$ is in static equilibrium. Now, when $B$ is released, its acceleration immediately after the release is $b$. The value of $\frac{a}{b}$ is (pulley, string and the spring are massless)

The same spring is attached with $2 \mathrm{kg}$, $3 \mathrm{kg}$ and $1 \mathrm{kg}$ blocks in three different cases, as shown in the figure. If $x_1$, $x_2$ and $x_3$ are the extensions in the spring in these cases, then (Assume all the blocks to move with uniform acceleration)

The figure shows a $5 \mathrm{kg}$ ladder hanging from a string that is connected with the ceiling and is having a spring balance connected in between. A boy of mass $25 \mathrm{kg}$ is climbing up the ladder at acceleration $1 \mathrm{m} {\mathrm{s}}^{-2}$. Assuming the spring balance and the string to be massless and the spring to show a constant reading, the reading of the spring balance is (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Two blocks of mass $M$ and $m$ are used to compress two different massless springs, as shown. The left spring is compressed by, $3 \mathrm{cm}$ while the right spring is compressed by an unknown amount. The system is at rest and all surfaces are fixed and smooth. Which of the following statements are true?