An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are 1 kg first part moving with a velocity of 12 ms^-1 and 2 kg second part moving with a velocity of 8 ms^-1.If the third part flies off with a velocity of 4 ms^-,its mass would be

• 5 kg 

• 7 kg

• 17 kg

• 17 kg

If the dimensions of a physical quantity are given by M^a L^b T^c, the physical quantity will be 

• pressure if a = 1, b = -1, c= 2

• velocity if a = 1, b = 1, c = -2

• acceleration if a = 1, b = 1, c =-2

• acceleration if a = 1, b = 1, c =-2

Under the influence of a uniform magnetic field, a charged particle moves with constant speed v in a circle of radius R. The time period of rotation of the particle

• depends on v and not on R

• depends on R and not on v

• is independent of both v and R

• is independent of both v and R

A body mass 1 kg is thrown upwards with velocity 20 ms^-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?  (g = 10 ms^-2)

• 20 J

• 30 J

• 40 J

• 40 J

The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, then its acceleration is 

• 30 ms^-2 downward

• 4 ms^-2  upwards

•  4 ms^-2  downwards

•  4 ms^-2  downwards

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 s is s₁ and that covered in the first 20 s is s₂, then

• s₂ = 2s₁

• s₂ = 3s₁

• s₂ = 4 s₁

• s₂ = 4 s₁

A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring. the ring will then rotate with an angular velocity

Two bodies of mass 1 kg have position vectors,  respectively.The centre of mass of this system has a position vector

Four identical thin rods each of mass M and length l , inertial form a square frame. moment of inertia of this frame about an axis through the centre of the square and perpendicular to this plane is 

• 4Ml²/3

• 2Ml²/3

• 13Ml²/3

• 13Ml²/3

The figure shows elliptical orbit of a planet m about the sun S. The shaded are SCD is twice the shaded area SAB. If t₁ is the time for the planet to move from C to D and t₂ is the time to move from A to B then,

• t₁ > t₂

• t₁ =4 t₂

• t₁ = 2t₂

• t₁ = 2t₂