List of top Physics Questions on Radioactivity asked in JEE Advanced

A table tennis ball has radius \( \frac{3}{2} \times 10^{-2} \, \text{m} \) and mass \( \frac{22}{7} \times 10^{-3} \, \text{kg} \). It is slowly pushed down into a swimming pool to a depth \( d = 0.7 \, \text{m} \) below the water surface and then released from rest. It emerges from the water surface at speed \( v \), without getting wet, and rises to a height \( H \). Which of the following option(s) is(are) correct?\(\text{(Given: } \pi = \frac{22}{7}, g = 10 \, \text{m/s}^2, \text{density of water} = 1 \times 10^3 \, \text{kg/m}^3, \text{viscosity of water} = 1 \times 10^{-3} \, \text{Pa.s).}\)
A spherical soap bubble inside an air chamber at pressure \(P_0 = 10^5 \, \text{Pa}\) has a certain radius so that the excess pressure inside the bubble is \(\Delta P = 144 \, \text{Pa}\). Now, the chamber pressure is reduced to \(8P_0/27\) so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure \(\Delta P\) in both the cases to be much smaller than the chamber pressure. The new excess pressure \(\Delta P\) in \(\text{Pa}\) is \_\_\_\_.
A ball is thrown from the location \((x_0, y_0) = (0, 0)\) of a horizontal playground with an initial speed \(v_0\) at an angle \(\theta_0\) from the \(+x\)-direction. The ball is to be hit by a stone, which is thrown at the same time from the location \((x_1, y_1) = (L, 0)\). The stone is thrown at an angle \((180^\circ - \theta_1)\) from the \(+x\)-direction with a suitable initial speed. For a fixed \(v_0\), when \((\theta_0, \theta_1) = (45^\circ, 45^\circ)\), the stone hits the ball after time \(T_1\), and when \((\theta_0, \theta_1) = (60^\circ, 30^\circ)\), it hits the ball after time \(T_2\). In such a case, \(\left(\frac{T_1}{T_2}\right)^2\) is \_\_\_\_.
A region in the form of an equilateral triangle (in x-y plane) of height \( L \) has a uniform magnetic field \( \mathbf{B} \) pointing in the \( +z \)-direction. A conducting loop PQR, in the form of an equilateral triangle of the same height \( L \), is placed in the x-y plane with its vertex \( P \) at \( x = 0 \) in the orientation shown in the figure. At \( t = 0 \), the loop starts entering the region of the magnetic field with a uniform velocity \( \mathbf{v} \) along the \( +x \)-direction. The plane of the loop and its orientation remain unchanged throughout its motion. 
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Which of the following graphs best depicts the variation of the induced emf (\( \mathcal{E} \)) in the loop as a function of the distance (\( x \)) starting from \( x = 0 \)?
An infinitely long thin wire, having a uniform charge density per unit length of \(5 \, \text{nC/m}\), is passing through a spherical shell of radius \(1 \, \text{m}\), as shown in the figure. A \(10 \, \text{nC}\) charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points \(P\) and \(R\), in Volt, is ______. \[ \text{(Given: In SI units } \frac{1}{4\pi\epsilon_0} = 9 \times 10^9, \ln 2 = 0.7). \] Ignore the area pierced by the wire.
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The \(8^\text{th}\) bright fringe above the point \( O \) oscillates with time between two extreme positions. The separation between these two extreme positions, in micrometer (\(\mu \text{m}\)), is.
The maximum speed in \(\mu\text{m/s}\) at which the \(8^\text{th}\) bright fringe will move is .
If the collision occurs at time \(t = 0\), the value of \(v_{\text{cm}} / (a\omega)\) will be .
If the collision occurs at time \( t_0 = \frac{\pi}{2\omega} \), then the value of \( \frac{4b^2}{a^2} \) will be:
The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be \(20.0 \, \text{cm}\). The maximum percentage error in the determination of the volume is \_\_\_\_.
The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction  \(^{16}_{7}\text{N} + ^{4}_{2}\text{He} \rightarrow ^{1}_{1}\text{H} + ^{19}_{8}\text{O}\) in a laboratory frame is n (in MeV). Assume that \(^{16}_{7}\text{N}\) is at rest in the laboratory frame. The masses of  \(^{16}_{7}\text{N} , ^{4}_{2}\text{He} , ^{1}_{1}\text{H}\ \text{and}\ ^{19}_{8}\text{O}\) can be taken to be 16.006u,4.003u, 1.008u and 19.003u, respectively, where 1u=930MeVc−2. The value of n is ________
In a radioactive decay chain reaction, ${ }_{90}^{230} Th$ nucleus decays into ${ }_{84}^{214} Po$ nucleus. The ratio of the number of $\alpha$ to number of $\beta^{-}$particles emitted in this process is _____