The trajectory of a charged particle in a uniform magnetic field depends on the angle between its velocity vector and the magnetic field vector. We need to analyze the force exerted by the magnetic field and its effect on the particle's motion.
Lorentz Force: When a charged particle with charge \(q\) and velocity \(\vec{v}\) moves in a magnetic field \(\vec{B}\), it experiences a magnetic force \(\vec{F}\) given by the Lorentz force formula:
\[ \vec{F} = q(\vec{v} \times \vec{B}) \]Direction of Force: The force \(\vec{F}\) is always perpendicular to both the velocity \(\vec{v}\) and the magnetic field \(\vec{B}\). This means the magnetic force does no work on the particle (since \(\vec{F} \cdot \vec{v} = 0\)) and therefore does not change the magnitude of the particle's velocity (its kinetic energy remains constant).
Case 1: Velocity parallel or anti-parallel to the magnetic field.
If \(\vec{v}\) is parallel or anti-parallel to \(\vec{B}\), then \(\vec{v} \times \vec{B} = 0\). In this case, the magnetic force \(\vec{F} = 0\). The particle will continue to move in a straight line with constant velocity.
Case 2: Velocity perpendicular to the magnetic field.
If \(\vec{v}\) is perpendicular to \(\vec{B}\), the force \(\vec{F}\) is always perpendicular to \(\vec{v}\) and has a constant magnitude \(F = qvB\). This force acts as a centripetal force, causing the particle to move in a circular path. The radius of this circular path is given by:
Case 3: Velocity at an angle to the magnetic field.
If the velocity \(\vec{v}\) makes an angle \(\theta\) (where \(0 < \theta < 90^\circ\)) with the magnetic field \(\vec{B}\), we can resolve the velocity into two components:
The combination of these two motions (uniform linear motion along the field and circular motion perpendicular to the field) results in a helical path. The pitch of the helix (distance traveled along the field in one revolution) is \(p = v_{\parallel} T\), where \(T = \frac{2\pi m}{qB}\) is the period of the circular motion.
A) Helical path: As explained in Case 3, when a charged particle's velocity is at an angle to the uniform magnetic field, its motion can be decomposed into a uniform linear motion along the field and a circular motion perpendicular to the field, resulting in a helical trajectory. If the velocity is strictly perpendicular, it's a circular path (a special case of a helix with zero pitch). If the velocity is strictly parallel, it's a straight line (a helix with infinite radius).
What is the main feature of the 106th Constitutional Amendment Act, 2023?
Set up of the Lokpal
Reservation of one-third seats for women in legislatures
Provision of legal status to Right to Property
Abolishment of titles
The question asks for the main feature of the 106th Constitutional Amendment Act, 2023. To answer this, one needs to recall the key provisions of this specific amendment.
Correct Option: B) Reservation of one-third seats for women in legislatures
The question asks to identify the primary type of natural vegetation found in the Western Ghats and the northeastern hills of India. This requires knowledge of the climatic conditions and corresponding vegetation types in these regions.
Correct Option: A) Tropical Evergreen Forests are found in areas receiving more than 200 cm of rainfall with a short dry season. The Western Ghats and the northeastern hills (like parts of Assam, Nagaland, Manipur, Mizoram, Tripura, and Meghalaya) receive abundant rainfall and maintain high temperatures, making them prime regions for this type of vegetation.
The question asks about a significant achievement in space technology: successfully docking two satellites in space. This is a complex maneuver that demonstrates advanced capabilities in rendezvous and proximity operations (RPO). We need to identify which nation achieved this milestone in January 2025, specifically becoming the fourth nation to do so.
D) India. India's ISRO is scheduled to conduct the SPADEX mission in January 2025, which aims to demonstrate autonomous rendezvous and docking of two satellites. If successful, India would be the fourth nation to achieve this capability.
The question asks to identify the honour awarded to Major Malla Rama Gopal Naidu in May 2025. This requires knowledge of recent military awards and current affairs.
B) Kirti Chakra. Major Malla Rama Gopal Naidu was awarded the Kirti Chakra for his gallantry in an anti-terrorist operation. This is a well-documented event in recent Indian military honours.
The question asks to identify which of the given options was NOT a major cause of people's revolts before 1857. We need to evaluate each option based on historical facts regarding the causes of pre-1857 uprisings in India.
Correct Option: C) Conversion of people to Christianity. While missionary activities and conversions did occur and could cause social tension, they were not a major, widespread cause for the numerous armed revolts and uprisings that characterized the period before 1857. The primary drivers of these revolts were economic exploitation, oppressive land revenue policies, and the destruction of traditional livelihoods.
The question asks to identify the recipient of the Honorary Palme d'Or at the 2025 Cannes Film Festival for lifetime achievement. This requires knowledge of recent major film festival awards.
Correct Option: B) Robert De Niro
Robert De Niro was announced as the recipient of the Honorary Palme d'Or at the 2025 Cannes Film Festival, recognizing his extensive career and contributions to cinema.
The question asks to identify the colonial-era building in Chennai that serves as the headquarters of the Greater Chennai Corporation. This requires knowledge of prominent historical buildings in Chennai and their current functions.
Correct Option: B) Ripon Building is the headquarters of the Greater Chennai Corporation. It is a prominent colonial-era building known for its Indo-Saracenic architecture.
The question asks about the launch of the Nationwide Mass Drug Administration Campaign for Lymphatic Filariasis. This requires knowledge of recent public health initiatives and the individuals responsible for launching them, typically Union Ministers related to Health and Family Welfare.
In February 2023, the Union Minister for Health and Family Welfare, Dr. Mansukh Mandaviya, launched the second phase of the annual Nationwide Mass Drug Administration (MDA) campaign for Lymphatic Filariasis. However, among the given options, Jagat Prakash Nadda has also served as the Union Minister for Health and Family Welfare and has been involved in similar public health initiatives. Specifically, he launched the campaign in 2015.
Correct Option: D) Jagat Prakash Nadda. Jagat Prakash Nadda, while serving as the Union Minister for Health and Family Welfare, launched the Nationwide Mass Drug Administration (MDA) Campaign for Lymphatic Filariasis in 2015. This campaign aimed to eliminate Lymphatic Filariasis by administering anti-filarial drugs to the population in endemic areas.
The question asks about the primary authority granted to the Governor of a State under the Fifth Schedule of the Indian Constitution concerning Scheduled Areas. This requires knowledge of the special provisions for the administration and control of Scheduled Areas and Scheduled Tribes.
Correct Option: B) Power to regulate land, forests and social customs in Scheduled Areas
This option accurately reflects the primary authority of the Governor under the Fifth Schedule. The Governor has the power to make regulations for the peace and good government of Scheduled Areas, which includes regulating land transfers, protecting tribal customs, and controlling activities like moneylending to safeguard tribal interests. While forests are not explicitly mentioned in the constitutional text regarding the Governor's regulation-making power, the overall intent of protecting tribal land and resources implicitly covers aspects related to forests in these areas, as tribal life is deeply intertwined with forest resources.