Instructions

For the following questions answer them individually

Question 41

A biconvex lens of focal length 15 cmis in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

Question 42

A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force Fit) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

Question 43

A tiny spherical oil drop carrying a net charge q is balanced instill air with a vertical uniform electric field of strength $$\frac{81 \pi}{7} \times 10^5 Vm^{-1}$$. When the field switched off, the drop is observed to fall with terminal velocity $$2 \times 10^{-3} m s^{-1}$$. Given $$g = 9.8 m s^{-2}$$, viscosity of the air = $$1.8 \times 10^{-5} Ns m^{-2}$$ and the density of oil = $$900 kg m^{-3}$$, the magnitude of q is

Question 44

A uniformly charged thin spherical shell of radius R carries uniform surface charge density of $$\sigma$$ per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to

Question 45

A diatomic ideal gas is compressed adiabatically to $$\frac{1}{32}$$ of its initial volume. In the initial temperature of the gas is $$T_i$$(in Kelvin) and the final temperature is $$aT_i$$, the value of a is

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Question 46

At time t = O, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V ?

[Take : $$\ln 5 = 1.6, \ln 3 = 1.1$$]

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Question 47

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $$\frac{25}{3} m$$ to $$\frac{50}{7} m$$ in 30 seconds. What is the speed of the object in km per hour ?

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Question 48

A large glass slab $$(\mu = \frac{5}{3})$$ of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R?

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Question 49

To determine the half life of a radioactive element, a student plots a graph of $$\ln \mid \frac{dN(t)}{dt} \mid$$ versus t. Here $$\frac{dN(t)}{dt}$$ is the rate of radioactive decay at time t If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is

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Instructions

When liquid medicine of density $$\rho$$ is to be put in theeye, it is done with the help of a dropper. As the bulb onthe topof the dropperis pressed, a drop forms at the opening of the dropper. We wishto estimate the size of the drop. Wefirst assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.

Question 50

If the radius of the opening of the dropperis r, the vertical force due to the surface tension on the drop of radius R (assuming $$r \ll R$$) is

CAT Averages, Ratios & Proportions

CAT Logarithms, Surds & Indices