A box of mass 2 kg is placed on the roof of a car. The box would remain stationary until the car attains a maximum acceleration. Coefficient of static friction between the box and the roof of the car is 0.2 and g = 10 ms^-2. This maximum acceleration of the car, for the box to remain stationary, is

• 8 ms^-2

• 6 ms^-2

• 4 ms^-2

• 2 ms^-2

The dimension of angular momentum is

• [M⁰L¹T^-1]

• [M¹L²T^-2]

• [M¹L²T¹]

• [M²L¹T^-2]

f A = B + C have scalar magnitudes of 5, 4, 3 units respectively, then the angle between A and C is

• cos^-1 (3/5)

• cos^-1 (4/5)

• π/2

• sin^-1 (3/4)

A particle is travelling along a straight line OX. The distance x (in metre) of the particle from O at a time t is given by x = 37 + 27t − t³, where t is time in seconds. The distance of the particle from O when it comes to rest is

• 81 m

• 91 m

• 101 m

• 111 m

A particle is projected from the ground with a kinetic energy E at an angle of 60° with the horizontal. Its kinetic energy at the highest point of its motion will be

• $\mathrm{E}/\sqrt{2}$

• E/2

• E/4

• E/8

A bullet on penetrating 30 cm into its target loses its velocity by 50%. What additional distance will it penetrate into the target before it comes to rest ?

• 30 cm

• 20 cm

• 10 cm

• 5 cm

Average distance of the Earth from the Sun is L₁. If one year of the Earth = D days, one year of another planet whose average distance from the Sun is L₂ will be

• $\mathrm{D} {\left(\frac{{\mathrm{L}}_2}{{\mathrm{L}}_1}\right)}^2 \mathrm{days}$

• $\mathrm{D} {\left(\frac{{\mathrm{L}}_2}{{\mathrm{L}}_1}\right)}^{3/2} \mathrm{days}$

• $\mathrm{D} {\left(\frac{{\mathrm{L}}_2}{{\mathrm{L}}_1}\right)}^{2/3} \mathrm{days}$

• $\mathrm{D} \left(\frac{{\mathrm{L}}_2}{{\mathrm{L}}_1}\right) \mathrm{days}$

A spherical ball A of mass 4 kg, moving along a straight line strikes another spherical ball B of mass 1 kg at rest. After the collision, A and B move with velocities v₁ ms^-1 and v₂ ms^-1 respectively making angles of 30° and 60° with respect to the original direction of motion of A. The ratio $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}$ will be

• $\frac{\sqrt{3}}{4}$

• $\frac{4}{\sqrt{3}}$

• $\frac{1}{\sqrt{3}}$

• $\sqrt{3}$

In a slide caliper, (m + 1) number of vernier divisions is equal to m number of smallest main scale divisions. If d unit is the magnitude of the smallest main scale division, then the magnitude of the vernier constant is

• d / (m + 1) unit

• d / m unit

• md / (m + 1) unit

• (m + 1)d / m unit

From the top of a tower, 80 m high from the ground, a stone is thrown in the horizontal direction with a velocity of 8 ms^-1 . The stone reaches the ground after a time 't' and falls at a distance of 'd' from the foot of the tower. Assuming g = 10 m/s², the time t and distance d are given respectively by

• 6 s, 64 m

• 6 s, 48 m

• 4 s, 32 m

• 4 s, 16 m