Intuitive Concepts of Force and Inertia

A monkey of mass $20 \mathrm{kg}$ is holding a vertical rope. The rope will not break when a mass of $25 \mathrm{kg}$ is suspended from it but will break if the mass exceeds $25 \mathrm{kg}$. What is the maximum acceleration with which the monkey can climb up along the rope? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Block $A$ of mass $m$ and block $B$ of mass $2m$ are placed on a fixed triangular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45°$ to the horizontal on both sides. The coefficient of friction between block $A$ and the wedge is $\frac{2}{3}$ and that between block $B$ and the wedge is $\frac{1}{3}$. If the system of $A$ and $B$ is released from rest, find the magnitude and direction of the force of friction acting on $A.$

Two blocks of mass $2.9 \mathrm{kg}$ and $1.9 \mathrm{kg}$ are suspended from a rigid support $S$ by two inextensible wires each of length $1 \mathrm{m}$ see figure. The upper wire has negligible mass and the lower wire has a uniform mass of $0.2 \mathrm{kg}{\mathrm{m}}^{-1}$ . The whole system of blocks, wires and support has an upward acceleration of $0.2 \mathrm{m}{\mathrm{s}}^{-2}$ . Acceleration due to gravity is $9.8 \mathrm{m}{\mathrm{s}}^{-2}$ .

(i) Find the tension $T$ at the mid-point of the lower wire.

(ii) Find the tension  $T^{\text{'}}$  at the mid-point of the upper wire.

A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K_1$ and $K_2.$ For the frictionless surface, the time period of oscillation of mass $m$ is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : An electric fan continues to rotate for some time after the current is switched off.

Reason R: Fan continues to rotate due to inertia of motion.

In the light of above statements, choose the most appropriate answer from the options given below.

A body of mass $5 \mathrm{kg}$ is in equilibrium due to forces $F_1, F_2$ and $F_3$. $F_2$ and $F_3$ are perpendicular to each other. If $F_1$ is removed then find the acceleration of body. Given $F_2= 6 \mathrm{N}$ and $F_3=8 \mathrm{N}$.

For the situation shown in the figure, horizontal spring and the spring connecting blocks $B$ and $C$ are light. The blocks $A,B$ and $C$ are of same mass $m$. The pulley is smooth and fixed. The accelerations of $A, B$ and $C$ just after cutting the horizontal spring are

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The system shown in figure is in equilibrium initially. String connecting blocks is cut at $t=0$. Magnitude of the relative acceleration of blocks (in $\mathrm{m} {\mathrm{s}}^{-2}$) just after the string is cut is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half the length, the line $OA$ will:

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A $10\mathrm{kg}$ mass is stationary in the position shown. Each of the three springs are relaxed. Each spring has a characteristic stiffness constant $k$, as shown on the diagram. If the mass is now displaced $20\mathrm{mm}$ to the right, what will be the net force, in newtons, exerted by the three springs on the mass? Ignore gravity

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The force exerted by a special compression device is given as function of compression $x$ as $F_x\left(x\right)=kx\left(x-l\right)$ for $0\le x\le l$, where $l$ is the maximum possible compression and $k$ is a constant. The force exerted by the device under compression is maximum when compression is:

In the given diagram system is in equilibrium. If applied force $F$ is doubled how much distance, the mass less block will more towards right before new equilibrium is achieved.

If a spring of stiffness '$k$' is cut into two parts '$A$' and '$B$' of length $l_A:l_B=2:3$, then the stiffness of spring '$A$' is given by:

Two blocks $A$ and $B$ of equal mass $2\mathrm{kg}$ are arranged as shown with springs $S_1$ and $S_2$. Spring $S_2$ is pulled with force $F=6 \mathrm{N}$. Acceleration of block $B$ is $4 \mathrm{m} {\mathrm{s}}^{-2}$ towards right at an instant. If $F$ is suddenly removed at this instant, the instantaneous acceleration of $A$ and $B$ will be (assume no friction)

A box is pulled with force of $200 \mathrm{N}$ at angle of $60°$ above the horizontal. Then the horizontal and vertical components of the force are