Mechanics – Page 3

JEE Advanced 2019 Paper 1, Question 14

A block of weight $100$ N is suspended by copper and steel wires of same cross sectional area $0.5$ cm $^2$ and, length $\sqrt{3}$ m and $1$ m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are $30^{\circ}$ and $60^{\circ}$ , respectively.
If elongation in copper wire is $\left(\Delta l_{C}\right)$ and elongation in steel wire is $\left(\Delta l_{S}\right)$ , then the ratio $\frac{\Delta l_{C}}{\Delta l_{S}}$ is

[Young’s modulus for copper and steel are $1 \times 10^{11}$ N/m $^2$ and $2 \times 10^{11}$ N/m $^2$ , respectively.]

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Solution

We will label the tension in the steel and copper wires by $F_S$ and …

JEE Advanced 2019 Paper 1, Question 1

Consider a spherical gas cloud of mass density $\rho(r)$ in free space where $r$ is the radial distance from its center. The gaseous cloud is made of particles of equal mass $m$ moving in circular orbits about the common center with the same kinetic energy $K$ . The force acting on the particles is their mutual gravitational force. If $\rho(r)$ is constant in time, the particle number density $n(r) = \rho(r)/m$ is [ $G$ is the universal gravitational constant]