Physics

A metallic sphere cools from ${50}^{\circ }\mathrm{C}$ to ${40}^{\circ }$  in 300 s. If atmospheric temperature around is ${20}^{\circ }\mathrm{C}$   , then the sphere's temperature after the next 5 minutes will be close to:

A wire $A$ $$ , bent in the shape of an arc of a circle, carrying a current of $$ $2\mathrm{A}$ and having radius $2\mathrm{c}\mathrm{m}$ $$ and another wire $B$ $$ , also bent in the shape of arc of a circle, carrying a current of $3\mathrm{A}$ $$ and having radius of $4\mathrm{c}\mathrm{m}$ $$ , are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ $$ and B$$ at the common centre 0 is:

Two light waves having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first wave travels path $L_1$  through a medium of refractive index $n_1$    while the second wave travels a path of length $L_2$  through a medium of refractive index $n_2$ . After this the phase difference between the two waves is:

A block of mass $m$  attached to a massless spring is performing oscillatory motion of amplitude ' $A$ ' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become $fA$ . The value of $f$  is:

Particle $A$ $$ of mass $m_A=\frac{m}{2}$ ${}_{}\frac{}{}$ moving along the $x$ $$ -axis with velocity $v_0$ ${}_{}$ collides elastically with another particle $$ $B$ at rest having mass $m_B=\frac{m}{3}$ ${}_{}\frac{}{}$ . If both particles move along the $$ $x$ axis after the collision, the change $\mathrm{\Delta }\lambda$ $$ in de-Broglie wavelength of particle $A$ $$ , in terms of its de-Broglie wavelength $\left({}_{}\right)$ $\left({\lambda }_0\right)$ before collision is:

Concentric metallic hollow spheres of radii   $R$ and $4R$    hold charges $Q_1$ and ${\mathrm{Q}}_2$  respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $V\left(R\right)-V\left(4R\right)$  is:

Two sources of light emit $X$  - rays of wavelength   $1\mathrm{n}\mathrm{m}$ and visible light of wavelength $500\mathrm{n}\mathrm{m}$   , respectively. Both the sources emit light of the same power $200\mathrm{W}$   . The ratio of the number density of photons of $X$  - rays to the number density of photons of the visible light of the given wavelengths is:

Dimensional formula for thermal conductivity is (here K$$ denotes the temperature):

Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a component, are just reversed?

A Tennis ball is released from a height $h$ $$ and after freely falling on a wooden floor it rebounds and reaches height $\frac{h}{2}$ $\frac{}{}$ . The velocity versus height of the ball during its motion may be represented graphically by:

(graphs are drawn schematically and on not to scale)